Sequences

392,541 sequences

Expansion of exp(sin(x)*cosh(x)).A009211
Expansion of exp(sin(x)*cosh(x)).
E.g.f. exp(sin(x)*exp(x)).A009212
E.g.f. exp(sin(x)*exp(x)).
a(n) = gcd(d(n), phi(n)), where d is the number of divisors of n (A000005) and phi is Euler's totient function (A000010).A009213
a(n) = gcd(d(n), phi(n)), where d is the number of divisors of n (A000005) and phi is Euler's totient function (A000010).
E.g.f. exp(x*sin(x)) (even powers only).A009214
E.g.f. exp(x*sin(x)) (even powers only).
Expansion of e.g.f.: exp(sin(x)/cosh(x)).A009215
Expansion of e.g.f.: exp(sin(x)/cosh(x)).
E.g.f.: exp(sin(x)/exp(x)).A009216
E.g.f.: exp(sin(x)/exp(x)).
E.g.f. exp(sin(x)^2) (even powers only).A009217
E.g.f. exp(sin(x)^2) (even powers only).
Expansion of e.g.f. exp(sinh(log(1+x))).A009218
Expansion of e.g.f. exp(sinh(log(1+x))).
Expansion of e.g.f.: exp(sinh(sin(x))).A009219
Expansion of e.g.f.: exp(sinh(sin(x))).
Sum(a(n)*x^n/n!) = exp(sinh(sinh(x))).A009220
Sum(a(n)*x^n/n!) = exp(sinh(sinh(x))).
Expansion of exp(sinh(tan(x))).A009221
Expansion of exp(sinh(tan(x))).
Expansion of e.g.f.: exp(sinh(tanh(x))).A009222
Expansion of e.g.f.: exp(sinh(tanh(x))).
a(n) = gcd(sigma(n), phi(n)).A009223
a(n) = gcd(sigma(n), phi(n)).
Expansion of exp(sinh(x))*x.A009224
Expansion of exp(sinh(x))*x.
Expansion of exp(sinh(x))/cos(x).A009225
Expansion of exp(sinh(x))/cos(x).
Expansion of e.g.f.: exp(sinh(x))/cosh(x).A009226
Expansion of e.g.f.: exp(sinh(x))/cosh(x).
Expansion of e.g.f.: exp(sinh(x))/exp(x).A009227
Expansion of e.g.f.: exp(sinh(x))/exp(x).
Expansion of e.g.f.: exp(sinh(x)*cos(x)).A009228
Expansion of e.g.f.: exp(sinh(x)*cos(x)).
Expansion of e.g.f. exp(sinh(x)*cosh(x)).A009229
Expansion of e.g.f. exp(sinh(x)*cosh(x)).
a(n) = lcm(n, d(n)).A009230
a(n) = lcm(n, d(n)).
Expansion of exp(sinh(x)*log(1+x)).A009231
Expansion of exp(sinh(x)*log(1+x)).
Expansion of exp(sinh(x)*sin(x)).A009232
Expansion of exp(sinh(x)*sin(x)).
Expansion of e.g.f. exp(sinh(x)*x) (even powers only).A009233
Expansion of e.g.f. exp(sinh(x)*x) (even powers only).
Expansion of e.g.f.: exp(sinh(x)/cos(x)).A009234
Expansion of e.g.f.: exp(sinh(x)/cos(x)).
E.g.f. exp( sinh(x) / exp(x) ) = exp( (1-exp(-2*x))/2 ).A009235
E.g.f. exp( sinh(x) / exp(x) ) = exp( (1-exp(-2*x))/2 ).
E.g.f. exp(sinh(x)^2) (even powers only).A009236
E.g.f. exp(sinh(x)^2) (even powers only).
Expansion of exp(tan(log(1+x))).A009237
Expansion of exp(tan(log(1+x))).
Expansion of e.g.f. exp(tan(sin(x))).A009238
Expansion of e.g.f. exp(tan(sin(x))).
Expansion of e.g.f.: exp(tan(sinh(x))).A009239
Expansion of e.g.f.: exp(tan(sinh(x))).
Expansion of exp(tan(tan(x))).A009240
Expansion of exp(tan(tan(x))).
Expansion of e.g.f.: exp(tan(tanh(x))).A009241
Expansion of e.g.f.: exp(tan(tanh(x))).
a(n) = lcm(n, sigma(n)).A009242
a(n) = lcm(n, sigma(n)).
Expansion of exp(tan(x))*x.A009243
Expansion of exp(tan(x))*x.
Expansion of e.g.f.: exp(tan(x))/cos(x).A009244
Expansion of e.g.f.: exp(tan(x))/cos(x).
Expansion of exp(tan(x))/cosh(x).A009245
Expansion of exp(tan(x))/cosh(x).
Expansion of exp(tan(x))/exp(x).A009246
Expansion of exp(tan(x))/exp(x).
Expansion of exp(tan(x)*cosh(x)).A009247
Expansion of exp(tan(x)*cosh(x)).
Expansion of e.g.f.: exp(tan(x).exp(x)).A009248
Expansion of e.g.f.: exp(tan(x).exp(x)).
E.g.f. exp(tan(x)*log(1+x)).A009249
E.g.f. exp(tan(x)*log(1+x)).
E.g.f. exp(tan(x)*sin(x)) (even powers only).A009250
E.g.f. exp(tan(x)*sin(x)) (even powers only).
Expansion of exp(tan(x)*sinh(x)).A009251
Expansion of exp(tan(x)*sinh(x)).
E.g.f. exp(x*tan(x)) (even powers only).A009252
E.g.f. exp(x*tan(x)) (even powers only).
Expansion of exp(tan(x)/cos(x)).A009253
Expansion of exp(tan(x)/cos(x)).
Expansion of exp(tan(x)/cosh(x)).A009254
Expansion of exp(tan(x)/cosh(x)).
Expansion of exp(tan(x)/exp(x)).A009255
Expansion of exp(tan(x)/exp(x)).
Expansion of e.g.f. exp(tan(x)^2) (even powers only).A009256
Expansion of e.g.f. exp(tan(x)^2) (even powers only).
Expansion of e.g.f. exp(tanh(log(1+x))).A009257
Expansion of e.g.f. exp(tanh(log(1+x))).
Expansion of exp(tanh(sin(x))).A009258
Expansion of exp(tanh(sin(x))).
Expansion of exp(tanh(sinh(x))).A009259
Expansion of exp(tanh(sinh(x))).
Expansion of exp(tanh(tan(x))).A009260
Expansion of exp(tanh(tan(x))).