Sequences

392,541 sequences

cosh(sec(x)*arctan(x))=1+1/2!*x^2+5/4!*x^4+205/6!*x^6+2473/8!*x^8...A012811
cosh(sec(x)*arctan(x))=1+1/2!*x^2+5/4!*x^4+205/6!*x^6+2473/8!*x^8...
sec(sec(x)*arctan(x))=1+1/2!*x^2+9/4!*x^4+345/6!*x^6+14833/8!*x^8...A012812
sec(sec(x)*arctan(x))=1+1/2!*x^2+9/4!*x^4+345/6!*x^6+14833/8!*x^8...
sech(sec(x)*arctan(x))=1-1/2!*x^2+1/4!*x^4-145/6!*x^6+6977/8!*x^8...A012813
sech(sec(x)*arctan(x))=1-1/2!*x^2+1/4!*x^4-145/6!*x^6+6977/8!*x^8...
Take every 5th term of Padovan sequence A000931, beginning with the third term.A012814
Take every 5th term of Padovan sequence A000931, beginning with the third term.
arcsin(sec(x)*sinh(x))=x+5/3!*x^3+85/5!*x^5+3985/7!*x^7+379625/9!*x^9...A012815
arcsin(sec(x)*sinh(x))=x+5/3!*x^3+85/5!*x^5+3985/7!*x^7+379625/9!*x^9...
E.g.f. arctan(sec(x)*sinh(x)) (odd powers only).A012816
E.g.f. arctan(sec(x)*sinh(x)) (odd powers only).
arcsinh(sec(x)*sinh(x))=x+3/3!*x^3+5/5!*x^5-217/7!*x^7+2505/9!*x^9...A012817
arcsinh(sec(x)*sinh(x))=x+3/3!*x^3+5/5!*x^5-217/7!*x^7+2505/9!*x^9...
arctanh(sec(x)*sinh(x))=x+6/3!*x^3+140/5!*x^5+8456/7!*x^7...A012818
arctanh(sec(x)*sinh(x))=x+6/3!*x^3+140/5!*x^5+8456/7!*x^7...
E.g.f.: sec(sec(x)*sinh(x))=1+1/2!*x^2+21/4!*x^4+837/6!*x^6+60585/8!*x^8...A012819
E.g.f.: sec(sec(x)*sinh(x))=1+1/2!*x^2+21/4!*x^4+837/6!*x^6+60585/8!*x^8...
sech(sec(x)*sinh(x))=1-1/2!*x^2-11/4!*x^4-37/6!*x^6+7145/8!*x^8...A012820
sech(sec(x)*sinh(x))=1-1/2!*x^2-11/4!*x^4-37/6!*x^6+7145/8!*x^8...
Expansion of e.g.f. exp(sec(x)*arcsinh(x)).A012821
Expansion of e.g.f. exp(sec(x)*arcsinh(x)).
sin(sec(x)*arcsinh(x))=x+1/3!*x^3+5/5!*x^5-499/7!*x^7-12055/9!*x^9...A012822
sin(sec(x)*arcsinh(x))=x+1/3!*x^3+5/5!*x^5-499/7!*x^7-12055/9!*x^9...
Expansion of e.g.f. arcsin(sec(x)*arcsinh(x)) (odd powers only).A012823
Expansion of e.g.f. arcsin(sec(x)*arcsinh(x)) (odd powers only).
tan(sec(x)*arcsinh(x))=x+4/3!*x^3+80/5!*x^5+3176/7!*x^7+240128/9!*x^9...A012824
tan(sec(x)*arcsinh(x))=x+4/3!*x^3+80/5!*x^5+3176/7!*x^7+240128/9!*x^9...
Expansion of e.g.f. of arctan(sec(x)*arcsinh(x)) (odd coefficients only).A012825
Expansion of e.g.f. of arctan(sec(x)*arcsinh(x)) (odd coefficients only).
cos(sec(x)*arcsinh(x))=1-1/2!*x^2-7/4!*x^4-145/6!*x^6-2063/8!*x^8...A012826
cos(sec(x)*arcsinh(x))=1-1/2!*x^2-7/4!*x^4-145/6!*x^6-2063/8!*x^8...
sinh(sec(x)*arcsinh(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+56697/9!*x^9...A012827
sinh(sec(x)*arcsinh(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+56697/9!*x^9...
arcsinh(sec(x)*arcsinh(x))=x+1/3!*x^3+13/5!*x^5-163/7!*x^7+12409/9!*x^9...A012828
arcsinh(sec(x)*arcsinh(x))=x+1/3!*x^3+13/5!*x^5-163/7!*x^7+12409/9!*x^9...
tanh(sec(x)*arcsinh(x))=x-504/7!*x^7+11904/9!*x^9-1023616/11!*x^11...A012829
tanh(sec(x)*arcsinh(x))=x-504/7!*x^7+11904/9!*x^9-1023616/11!*x^11...
arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7...A012830
arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7...
cosh(sec(x)*arcsinh(x))=1+1/2!*x^2+9/4!*x^4+225/6!*x^6+6993/8!*x^8...A012831
cosh(sec(x)*arcsinh(x))=1+1/2!*x^2+9/4!*x^4+225/6!*x^6+6993/8!*x^8...
sec(sec(x)*arcsinh(x))=1+1/2!*x^2+13/4!*x^4+445/6!*x^6+24953/8!*x^8...A012832
sec(sec(x)*arcsinh(x))=1+1/2!*x^2+13/4!*x^4+445/6!*x^6+24953/8!*x^8...
sech(sec(x)*arcsinh(x))=1-1/2!*x^2-3/4!*x^4-45/6!*x^6+2457/8!*x^8...A012833
sech(sec(x)*arcsinh(x))=1-1/2!*x^2-3/4!*x^4-45/6!*x^6+2457/8!*x^8...
arcsin(sec(x)*tanh(x))=x+2/3!*x^3+40/5!*x^5+1192/7!*x^7+87680/9!*x^9...A012834
arcsin(sec(x)*tanh(x))=x+2/3!*x^3+40/5!*x^5+1192/7!*x^7+87680/9!*x^9...
arctan(sec(x)*tanh(x))=x-1/3!*x^3+25/5!*x^5-761/7!*x^7+42065/9!*x^9...A012835
arctan(sec(x)*tanh(x))=x-1/3!*x^3+25/5!*x^5-761/7!*x^7+42065/9!*x^9...
arcsinh(sec(x)*tanh(x))=x+20/5!*x^5-280/7!*x^7+18000/9!*x^9...A012836
arcsinh(sec(x)*tanh(x))=x+20/5!*x^5-280/7!*x^7+18000/9!*x^9...
arctanh(sec(x)*tanh(x))=x+3/3!*x^3+65/5!*x^5+2723/7!*x^7...A012837
arctanh(sec(x)*tanh(x))=x+3/3!*x^3+65/5!*x^5+2723/7!*x^7...
sec(sec(x)*tanh(x))=1+1/2!*x^2+9/4!*x^4+297/6!*x^6+14385/8!*x^8...A012838
sec(sec(x)*tanh(x))=1+1/2!*x^2+9/4!*x^4+297/6!*x^6+14385/8!*x^8...
sech(sec(x)*tanh(x))=1-1/2!*x^2+1/4!*x^4-97/6!*x^6+2945/8!*x^8...A012839
sech(sec(x)*tanh(x))=1-1/2!*x^2+1/4!*x^4-97/6!*x^6+2945/8!*x^8...
exp(sec(x)*arctanh(x))=1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+120/5!*x^5...A012840
exp(sec(x)*arctanh(x))=1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+120/5!*x^5...
sin(sec(x)*arctanh(x))=x+4/3!*x^3+20/5!*x^5-1024/7!*x^7-147568/9!*x^9...A012841
sin(sec(x)*arctanh(x))=x+4/3!*x^3+20/5!*x^5-1024/7!*x^7-147568/9!*x^9...
arcsin(sec(x)*arctanh(x))=x+6/3!*x^3+128/5!*x^5+7000/7!*x^7...A012842
arcsin(sec(x)*arctanh(x))=x+6/3!*x^3+128/5!*x^5+7000/7!*x^7...
tan(sec(x)*arctanh(x))=x+7/3!*x^3+185/5!*x^5+11471/7!*x^7...A012843
tan(sec(x)*arctanh(x))=x+7/3!*x^3+185/5!*x^5+11471/7!*x^7...
arctan(sec(x)*arctanh(x))=x+3/3!*x^3-7/5!*x^5-917/7!*x^7-7183/9!*x^9...A012844
arctan(sec(x)*arctanh(x))=x+3/3!*x^3-7/5!*x^5-917/7!*x^7-7183/9!*x^9...
cos(sec(x)*arctanh(x))=1-1/2!*x^2-19/4!*x^4-565/6!*x^6-24743/8!*x^8...A012845
cos(sec(x)*arctanh(x))=1-1/2!*x^2-19/4!*x^4-565/6!*x^6-24743/8!*x^8...
sinh(sec(x)*arctanh(x))=x+6/3!*x^3+120/5!*x^5+5376/7!*x^7...A012846
sinh(sec(x)*arctanh(x))=x+6/3!*x^3+120/5!*x^5+5376/7!*x^7...
arcsinh(sec(x)*arctanh(x))=x+4/3!*x^3+28/5!*x^5+152/7!*x^7+6928/9!*x^9...A012847
arcsinh(sec(x)*arctanh(x))=x+4/3!*x^3+28/5!*x^5+152/7!*x^7+6928/9!*x^9...
tanh(sec(x)*arctanh(x))=x+3/3!*x^3-15/5!*x^5-1869/7!*x^7-88959/9!*x^9...A012848
tanh(sec(x)*arctanh(x))=x+3/3!*x^3-15/5!*x^5-1869/7!*x^7-88959/9!*x^9...
arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...A012849
arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...
cosh(sec(x)*arctanh(x))=1+1/2!*x^2+21/4!*x^4+765/6!*x^6+46473/8!*x^8...A012850
cosh(sec(x)*arctanh(x))=1+1/2!*x^2+21/4!*x^4+765/6!*x^6+46473/8!*x^8...
sec(sec(x)*arctanh(x))=1+1/2!*x^2+25/4!*x^4+1225/6!*x^6+108113/8!*x^8...A012851
sec(sec(x)*arctanh(x))=1+1/2!*x^2+25/4!*x^4+1225/6!*x^6+108113/8!*x^8...
sech(sec(x)*arctanh(x))=1-1/2!*x^2-15/4!*x^4-225/6!*x^6+3297/8!*x^8...A012852
sech(sec(x)*arctanh(x))=1-1/2!*x^2-15/4!*x^4-225/6!*x^6+3297/8!*x^8...
Expansion of sec(x)^2+sech(x)^2 in powers of x^4.A012853
Expansion of sec(x)^2+sech(x)^2 in powers of x^4.
Numerators of coefficients in Taylor series expansion of log(cosec(x)*log(x+1)).A012854
Numerators of coefficients in Taylor series expansion of log(cosec(x)*log(x+1)).
a(0) = 0, a(1) = 1, a(2) = 1; thereafter a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3).A012855
a(0) = 0, a(1) = 1, a(2) = 1; thereafter a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3).
Numerators of coefficients in Taylor series expansion of log(cosec(x)*arcsin(x)).A012856
Numerators of coefficients in Taylor series expansion of log(cosec(x)*arcsin(x)).
Numerator of [x^(2n)] of the Taylor expansion log(cosec(x)*arctan(x)).A012857
Numerator of [x^(2n)] of the Taylor expansion log(cosec(x)*arctan(x)).
Numerator of [x^(4n+2)] in the Taylor series log(cosec(x)*sinh(x)).A012858
Numerator of [x^(4n+2)] in the Taylor series log(cosec(x)*sinh(x)).
Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arcsinh(x)).A012859
Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arcsinh(x)).
Numerators of coefficients in Taylor series expansion of log(cosec(x)*tanh(x)).A012860
Numerators of coefficients in Taylor series expansion of log(cosec(x)*tanh(x)).