A302587 a(n) = n! * [x^n] exp(n*x)*tanh(x).

0, 1, 4, 25, 224, 2641, 38592, 671665, 13548544, 310580161, 7971353600, 226406902921, 7049219383296, 238722074157841, 8735529994928128, 343474252543881313, 14441163232204292096, 646510839624706118401, 30704150325602206089216, 1541807339347429264648441

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..386
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000182, A009832, A062024, A302583, A302584, A302585, A302586.

Programs

Maple

N:= 100: # to get a(0)..a(N)
T:= series(tanh(x),x,N+1):
C:= [seq(coeff(T,x,j),j=1..N)]:
seq(n! * add(C[i]*n^(n-i)/(n-i)!,i=1..n,2), n=0..N); # Robert Israel, Apr 10 2018

Mathematica

Table[n! SeriesCoefficient[Exp[n x] Tanh[x], {x, 0, n}], {n, 0, 19}]

PARI

a(n) = my(x='x+O('x^(n+1))); polcoeff(n!*exp(n*x)*tanh(x), n); \\ Michel Marcus, Apr 11 2018; corrected Jun 15 2022

Formula

a(n) ~ tanh(1) * n^n. - Vaclav Kotesovec, Jun 08 2019