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URL: https://oeis.org/A357591

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A357591
Expansion of e.g.f. (exp(x) - 1) * tan((exp(x) - 1)/2).
1
0, 0, 1, 3, 8, 25, 99, 476, 2643, 16575, 116002, 895719, 7554311, 69051034, 679913073, 7174562327, 80765185416, 966076987581, 12235992073975, 163590477924708, 2302288709067167, 34021599945907915, 526690307104399482, 8524372522971447683, 143963947160570293851
OFFSET
0,4
FORMULA
a(n) = 2 * Sum_{k=0..floor(n/2)} (-1)^k * Stirling2(n,2*k) * (1 - 4^k) * Bernoulli(2*k).
a(n) ~ n! * 2*Pi / ((Pi+1) * (log(1+Pi))^(n+1)).
MATHEMATICA
nmax = 20; CoefficientList[Series[(Exp[x] - 1)*Tan[(Exp[x] - 1)/2] , {x, 0, nmax}], x] * Range[0, nmax]!
Table[2*Sum[(-1)^k * StirlingS2[n, 2*k] * (1 - 4^k) * BernoulliB[2*k], {k, 0, n/2}], {n, 0, 20}]
PROG
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0], Vec(serlaplace((exp(x)-1)*tan((exp(x)-1)/2)))) \\ Seiichi Manyama, Oct 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 05 2022
STATUS
approved