Sequences

392,541 sequences

Expansion of e.g.f. sinh(arctanh(x) + log(x+1)).A013161
Expansion of e.g.f. sinh(arctanh(x) + log(x+1)).
Expansion of e.g.f. arcsinh(arctanh(x) + log(x+1)).A013162
Expansion of e.g.f. arcsinh(arctanh(x) + log(x+1)).
Expansion of e.g.f.: arctanh(arctanh(x)+log(x+1))=2*x-1/2!*x^2+20/3!*x^3-54/4!*x^4...A013163
Expansion of e.g.f.: arctanh(arctanh(x)+log(x+1))=2*x-1/2!*x^2+20/3!*x^3-54/4!*x^4...
cosh(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+51/4!*x^4-180/5!*x^5...A013164
cosh(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+51/4!*x^4-180/5!*x^5...
sec(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+115/4!*x^4-500/5!*x^5...A013165
sec(arctanh(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+115/4!*x^4-500/5!*x^5...
Expansion of e.g.f.: sech(arctanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+45/4!*x^4-300/5!*x^5...A013166
Expansion of e.g.f.: sech(arctanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+45/4!*x^4-300/5!*x^5...
Expansion of e.g.f. log(arctanh(x) + exp(x)).A013167
Expansion of e.g.f. log(arctanh(x) + exp(x)).
exp(arctanh(x)+sin(x))=1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+97/5!*x^5...A013168
exp(arctanh(x)+sin(x))=1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+97/5!*x^5...
arcsin(arctanh(x)+sin(x))=2*x+9/3!*x^3+353/5!*x^5+36799/7!*x^7...A013169
arcsin(arctanh(x)+sin(x))=2*x+9/3!*x^3+353/5!*x^5+36799/7!*x^7...
Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).A013170
Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).
sin(arctanh(x)+arcsin(x))=2*x-5/3!*x^3-55/5!*x^5-1535/7!*x^7...A013171
sin(arctanh(x)+arcsin(x))=2*x-5/3!*x^3-55/5!*x^5-1535/7!*x^7...
exp(arctanh(x)+tan(x))=1+2*x+4/2!*x^2+12/3!*x^3+48/4!*x^4+232/5!*x^5...A013172
exp(arctanh(x)+tan(x))=1+2*x+4/2!*x^2+12/3!*x^3+48/4!*x^4+232/5!*x^5...
arctan(arctanh(x)+tan(x))=2*x-12/3!*x^3+488/5!*x^5-48608/7!*x^7...A013173
arctan(arctanh(x)+tan(x))=2*x-12/3!*x^3+488/5!*x^5-48608/7!*x^7...
exp(arctanh(x) + arctan(x)) = 1 + 2*x + 4/2!*x^2 + 8/3!*x^3 + 16/4!*x^4 + 80/5!*x^5 +...A013174
exp(arctanh(x) + arctan(x)) = 1 + 2*x + 4/2!*x^2 + 8/3!*x^3 + 16/4!*x^4 + 80/5!*x^5 +...
sin(arctanh(x)+arctan(x))=2*x-8/3!*x^3+80/5!*x^5-4160/7!*x^7...A013175
sin(arctanh(x)+arctan(x))=2*x-8/3!*x^3+80/5!*x^5-4160/7!*x^7...
arcsin(arctanh(x)+arctan(x))=2*x+8/3!*x^3+336/5!*x^5+32832/7!*x^7...A013176
arcsin(arctanh(x)+arctan(x))=2*x+8/3!*x^3+336/5!*x^5+32832/7!*x^7...
tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7...A013177
tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7...
arctan(arctanh(x)+arctan(x))=2*x-16/3!*x^3+816/5!*x^5-100224/7!*x^7...A013178
arctan(arctanh(x)+arctan(x))=2*x-16/3!*x^3+816/5!*x^5-100224/7!*x^7...
cos(arctanh(x)+arctan(x))=1-4/2!*x^2+16/4!*x^4-640/6!*x^6+21760/8!*x^8...A013179
cos(arctanh(x)+arctan(x))=1-4/2!*x^2+16/4!*x^4-640/6!*x^6+21760/8!*x^8...
sec(arctanh(x)+arctan(x))=1+4/2!*x^2+80/4!*x^4+4480/6!*x^6...A013180
sec(arctanh(x)+arctan(x))=1+4/2!*x^2+80/4!*x^4+4480/6!*x^6...
Expansion of e.g.f.: log(arctanh(x)+cos(x)) = x-2/2!*x^2+7/3!*x^3-28/4!*x^4+193/5!*x^5...A013181
Expansion of e.g.f.: log(arctanh(x)+cos(x)) = x-2/2!*x^2+7/3!*x^3-28/4!*x^4+193/5!*x^5...
exp(arctanh(x)+sinh(x))=1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+177/5!*x^5...A013182
exp(arctanh(x)+sinh(x))=1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+177/5!*x^5...
exp(arctanh(x)+arcsinh(x)) = 1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+105/5!*x^5...A013183
exp(arctanh(x)+arcsinh(x)) = 1+2*x+4/2!*x^2+9/3!*x^3+24/4!*x^4+105/5!*x^5...
exp(arctanh(x)+tanh(x)) = 1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+72/5!*x^5...A013184
exp(arctanh(x)+tanh(x)) = 1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+72/5!*x^5...
E.g.f.: log(cosh(x)+log(x+1)).A013185
E.g.f.: log(cosh(x)+log(x+1)).
Expansion of e.g.f. log(cosh(x) + arcsin(x)).A013186
Expansion of e.g.f. log(cosh(x) + arcsin(x)).
Expansion of e.g.f. log(cosh(x) + tan(x)).A013187
Expansion of e.g.f. log(cosh(x) + tan(x)).
E.g.f.: log(cosh(x)+arctan(x))=x-3/3!*x^3+12/4!*x^4-7/5!*x^5-168/6!*x^6...A013188
E.g.f.: log(cosh(x)+arctan(x))=x-3/3!*x^3+12/4!*x^4-7/5!*x^5-168/6!*x^6...
All terms are squares and a(n) is length of n-th run.A013189
All terms are squares and a(n) is length of n-th run.
log(cosh(x)+arcsinh(x))=x-2/3!*x^3+8/4!*x^4-12/5!*x^5-48/6!*x^6...A013190
log(cosh(x)+arcsinh(x))=x-2/3!*x^3+8/4!*x^4-12/5!*x^5-48/6!*x^6...
Expansion of e.g.f. log(cosh(x) + tanh(x)).A013191
Expansion of e.g.f. log(cosh(x) + tanh(x)).
Expansion of e.g.f. log(cosh(x) + arctanh(x)).A013192
Expansion of e.g.f. log(cosh(x) + arctanh(x)).
Expansion of e.g.f. log(sec(x) + log(x+1)).A013193
Expansion of e.g.f. log(sec(x) + log(x+1)).
Expansion of e.g.f. log(sec(x) + sin(x)).A013194
Expansion of e.g.f. log(sec(x) + sin(x)).
E.g.f.: log(sec(x) + arcsin(x)).A013195
E.g.f.: log(sec(x) + arcsin(x)).
Expansion of e.g.f. log(sec(x) + arctan(x)).A013196
Expansion of e.g.f. log(sec(x) + arctan(x)).
Expansion of e.g.f. log(sec(x) + sinh(x)).A013197
Expansion of e.g.f. log(sec(x) + sinh(x)).
E.g.f.: log(sec(x)+arcsinh(x)) = x-2/3!*x^3+12/4!*x^4-32/5!*x^5+72/6!*x^6...A013198
E.g.f.: log(sec(x)+arcsinh(x)) = x-2/3!*x^3+12/4!*x^4-32/5!*x^5+72/6!*x^6...
Expansion of e.g.f. log(sec(x) + tanh(x)).A013199
Expansion of e.g.f. log(sec(x) + tanh(x)).
Expansion of e.g.f. log(sec(x)+arctanh(x)).A013200
Expansion of e.g.f. log(sec(x)+arctanh(x)).
log(sech(x)+log(x+1)) = x - 3/2!*x^2 + 10/3!*x^3 - 51/4!*x^4 + 373/5!*x^5 + ...A013201
log(sech(x)+log(x+1)) = x - 3/2!*x^2 + 10/3!*x^3 - 51/4!*x^4 + 373/5!*x^5 + ...
Expansion of e.g.f. log(sech(x) + sin(x)).A013202
Expansion of e.g.f. log(sech(x) + sin(x)).
Expansion of e.g.f. log(sech(x) + arcsin(x)).A013203
Expansion of e.g.f. log(sech(x) + arcsin(x)).
E.g.f. log(sech(x) + tan(x)).A013204
E.g.f. log(sech(x) + tan(x)).
Expansion of e.g.f. log(sech(x) + arctan(x)).A013205
Expansion of e.g.f. log(sech(x) + arctan(x)).
E.g.f.: log(sech(x)+sinh(x))=x-2/2!*x^2+6/3!*x^3-20/4!*x^4+120/5!*x^5...A013206
E.g.f.: log(sech(x)+sinh(x))=x-2/2!*x^2+6/3!*x^3-20/4!*x^4+120/5!*x^5...
Expansion of e.g.f.: log(sech(x)+arcsinh(x))=x-2/2!*x^2+4/3!*x^3-12/4!*x^4+68/5!*x^5...A013207
Expansion of e.g.f.: log(sech(x)+arcsinh(x))=x-2/2!*x^2+4/3!*x^3-12/4!*x^4+68/5!*x^5...
Expansion of e.g.f. log(sech(x) + tanh(x)).A013208
Expansion of e.g.f. log(sech(x) + tanh(x)).
Expansion of e.g.f. log(sech(x) + arctanh(x)).A013209
Expansion of e.g.f. log(sech(x) + arctanh(x)).
Expansion of e.g.f.: sin(log(x+1) - sin(x)) = -1/2!*x^2+3/3!*x^3-6/4!*x^4+23/5!*x^5...A013210
Expansion of e.g.f.: sin(log(x+1) - sin(x)) = -1/2!*x^2+3/3!*x^3-6/4!*x^4+23/5!*x^5...