A357591 Expansion of e.g.f. (exp(x) - 1) * tan((exp(x) - 1)/2).

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

Links

Table of n, a(n) for n=0..24.

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

Cf. A001469, A136128, A357240.

Sequence in context: A353406 A009268 A024430 * A182927 A012408 A184325

Adjacent sequences: A357588 A357589 A357590 * A357592 A357593 A357594

Keyword

nonn

Author

Vaclav Kotesovec, Oct 05 2022

Status

approved