Sequences

392,541 sequences

Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arctanh(x)).A012861
Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arctanh(x)).
Numerators of coefficients in Taylor series expansion of arccosh(cosec(x)*arctanh(x)).A012862
Numerators of coefficients in Taylor series expansion of arccosh(cosec(x)*arctanh(x)).
Numerators of coefficients in Taylor series expansion of log(cotan(x)*log(x+1)).A012863
Numerators of coefficients in Taylor series expansion of log(cotan(x)*log(x+1)).
Take every 5th term of Padovan sequence A000931, beginning with the first term.A012864
Take every 5th term of Padovan sequence A000931, beginning with the first term.
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsin(x)).A012865
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsin(x)).
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).A012866
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arctan(x)).A012867
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arctan(x)).
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsinh(x)).A012868
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsinh(x)).
Numerator of [x^(2n+1)] in the Taylor series arccos(cot(x)*arcsinh(x)).A012869
Numerator of [x^(2n+1)] in the Taylor series arccos(cot(x)*arcsinh(x)).
Numerator of [x^(4n+2)] in the Taylor series -log(cot(x)*tanh(x)).A012870
Numerator of [x^(4n+2)] in the Taylor series -log(cot(x)*tanh(x)).
Numerator of [x^(2n)] in the Taylor expansion log(cot(x)*arctanh(x)).A012871
Numerator of [x^(2n)] in the Taylor expansion log(cot(x)*arctanh(x)).
Expansion of e.g.f.: arcsin(sech(x)*log(x+1))=x-1/2!*x^2-6/4!*x^4+43/5!*x^5-195/6!*x^6...A012872
Expansion of e.g.f.: arcsin(sech(x)*log(x+1))=x-1/2!*x^2-6/4!*x^4+43/5!*x^5-195/6!*x^6...
Expansion of e.g.f.: arctan(sech(x)*log(x+1))=x-1/2!*x^2-3/3!*x^3+12/4!*x^4+43/5!*x^5...A012873
Expansion of e.g.f.: arctan(sech(x)*log(x+1))=x-1/2!*x^2-3/3!*x^3+12/4!*x^4+43/5!*x^5...
Expansion of e.g.f.: arcsinh(sech(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+33/5!*x^5...A012874
Expansion of e.g.f.: arcsinh(sech(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+33/5!*x^5...
Expansion of e.g.f.: arctanh(sech(x)*log(x+1))=x-1/2!*x^2+1/3!*x^3-12/4!*x^4+63/5!*x^5...A012875
Expansion of e.g.f.: arctanh(sech(x)*log(x+1))=x-1/2!*x^2+1/3!*x^3-12/4!*x^4+63/5!*x^5...
sec(sech(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...A012876
sec(sech(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...
Expansion of e.g.f.: sech(sech(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...A012877
Expansion of e.g.f.: sech(sech(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...
E.g.f.: exp(sech(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+5/5!*x^5...A012878
E.g.f.: exp(sech(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+5/5!*x^5...
Expansion of e.g.f.: exp(sech(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+20/5!*x^5...A012879
Expansion of e.g.f.: exp(sech(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+20/5!*x^5...
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).A012880
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
Expansion of e.g.f.: exp(sech(x)*arcsinh(x))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+5/5!*x^5...A012881
Expansion of e.g.f.: exp(sech(x)*arcsinh(x))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+5/5!*x^5...
Expansion of e.g.f.: exp(sech(x)*arctanh(x))=1+x+1/2!*x^2-3/4!*x^4+20/5!*x^5+165/6!*x^6...A012882
Expansion of e.g.f.: exp(sech(x)*arctanh(x))=1+x+1/2!*x^2-3/4!*x^4+20/5!*x^5+165/6!*x^6...
Numbers in which every prefix (in base 10) is 1 or a prime.A012883
Numbers in which every prefix (in base 10) is 1 or a prime.
Numbers such that every prefix and suffix is 1 or a prime.A012884
Numbers such that every prefix and suffix is 1 or a prime.
Suffixes of 357686312646216567629137 (all primes).A012885
Suffixes of 357686312646216567629137 (all primes).
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).A012886
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
exp(sin(x)+log(x+1))=1+2*x+3/2!*x^2+3/3!*x^3-3/4!*x^4-23/5!*x^5...A012887
exp(sin(x)+log(x+1))=1+2*x+3/2!*x^2+3/3!*x^3-3/4!*x^4-23/5!*x^5...
E.g.f.: sin(sin(x)+log(x+1))=2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4-13/5!*x^5...A012888
E.g.f.: sin(sin(x)+log(x+1))=2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4-13/5!*x^5...
Expansion of e.g.f. tan(sin(x) + log(x+1)).A012889
Expansion of e.g.f. tan(sin(x) + log(x+1)).
Expansion of e.g.f. arctan(sin(x) + log(x+1)).A012890
Expansion of e.g.f. arctan(sin(x) + log(x+1)).
Expansion of e.g.f.: cos(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+5/4!*x^4-10/5!*x^5...A012891
Expansion of e.g.f.: cos(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+5/4!*x^4-10/5!*x^5...
E.g.f.: sinh(sin(x)+log(x+1)).A012892
E.g.f.: sinh(sin(x)+log(x+1)).
arcsinh(sin(x)+log(x+1)) = 2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4+243/5!*x^5...A012893
arcsinh(sin(x)+log(x+1)) = 2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4+243/5!*x^5...
tanh(sin(x)+log(x+1))=2*x-1/2!*x^2-15/3!*x^3+42/4!*x^4+397/5!*x^5...A012894
tanh(sin(x)+log(x+1))=2*x-1/2!*x^2-15/3!*x^3+42/4!*x^4+397/5!*x^5...
Expansion of e.g.f.: arctanh(sin(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4+933/5!*x^5...A012895
Expansion of e.g.f.: arctanh(sin(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4+933/5!*x^5...
cosh(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+27/4!*x^4-150/5!*x^5...A012896
cosh(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+27/4!*x^4-150/5!*x^5...
sec(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+91/4!*x^4-470/5!*x^5...A012897
sec(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+91/4!*x^4-470/5!*x^5...
Expansion of e.g.f.: sech(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+69/4!*x^4-330/5!*x^5...A012898
Expansion of e.g.f.: sech(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+69/4!*x^4-330/5!*x^5...
E.g.f.: exp(arcsin(x)+log(x+1)).A012899
E.g.f.: exp(arcsin(x)+log(x+1)).
Expansion of e.g.f.: arcsin(arcsin(x)+log(x+1))=2*x-1/2!*x^2+11/3!*x^3-30/4!*x^4+471/5!*x^5...A012900
Expansion of e.g.f.: arcsin(arcsin(x)+log(x+1))=2*x-1/2!*x^2+11/3!*x^3-30/4!*x^4+471/5!*x^5...
Expansion of e.g.f. tan(arcsin(x) + log(x+1)).A012901
Expansion of e.g.f. tan(arcsin(x) + log(x+1)).
Expansion of e.g.f. arctan(arcsin(x) + log(x+1)).A012902
Expansion of e.g.f. arctan(arcsin(x) + log(x+1)).
Expansion of e.g.f.: cos(arcsin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3-11/4!*x^4+10/5!*x^5...A012903
Expansion of e.g.f.: cos(arcsin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3-11/4!*x^4+10/5!*x^5...
E.g.f.: sinh(arcsin(x)+log(x+1))=2*x-1/2!*x^2+11/3!*x^3-30/4!*x^4+215/5!*x^5...A012904
E.g.f.: sinh(arcsin(x)+log(x+1))=2*x-1/2!*x^2+11/3!*x^3-30/4!*x^4+215/5!*x^5...
Expansion of e.g.f: arcsinh(arcsin(x)+log(x+1))=2*x-1/2!*x^2-5/3!*x^3+18/4!*x^4+171/5!*x^5...A012905
Expansion of e.g.f: arcsinh(arcsin(x)+log(x+1))=2*x-1/2!*x^2-5/3!*x^3+18/4!*x^4+171/5!*x^5...
Expansion of e.g.f. tanh(arcsin(x) + log(x+1)).A012906
Expansion of e.g.f. tanh(arcsin(x) + log(x+1)).
Expansion of e.g.f. arctanh(arcsin(x) + log(x+1)).A012907
Expansion of e.g.f. arctanh(arcsin(x) + log(x+1)).
cosh(arcsin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+43/4!*x^4-170/5!*x^5...A012908
cosh(arcsin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+43/4!*x^4-170/5!*x^5...
sec(arcsin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+107/4!*x^4-490/5!*x^5...A012909
sec(arcsin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+107/4!*x^4-490/5!*x^5...
E.g.f.: sech(arcsin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+53/4!*x^4-310/5!*x^5...A012910
E.g.f.: sech(arcsin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+53/4!*x^4-310/5!*x^5...