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A302587
a(n) = n! * [x^n] exp(n*x)*tanh(x).
9
0, 1, 4, 25, 224, 2641, 38592, 671665, 13548544, 310580161, 7971353600, 226406902921, 7049219383296, 238722074157841, 8735529994928128, 343474252543881313, 14441163232204292096, 646510839624706118401, 30704150325602206089216, 1541807339347429264648441
OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) ~ tanh(1) * n^n. - Vaclav Kotesovec, Jun 08 2019
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}]
PROG
(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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 10 2018
STATUS
approved