A357649 Expansion of e.g.f. cosh( (exp(3*x) - 1)/3 ).

1, 0, 1, 9, 64, 435, 3097, 24822, 232759, 2517345, 30070954, 382827225, 5110770205, 71421582024, 1049487311485, 16286699945853, 267145966335088, 4616924929100535, 83622792656855125, 1578916985654901366, 30957723637379211115, 628927539690331202661

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/2)} 3^(n-2*k) * Stirling2(n,2*k).

a(n) ~ 3^n * exp(n/LambertW(3*n) - n - 1/3) * n^n / (LambertW(3*n)^n * 2*sqrt(1 + LambertW(3*n))). - Vaclav Kotesovec, Oct 07 2022

Mathematica

With[{m = 20}, Range[0, m]! * CoefficientList[Series[Cosh[(Exp[3*x] - 1)/3], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh((exp(3*x)-1)/3)))
(PARI) a(n) = sum(k=0, n\2, 3^(n-2*k)*stirling(n, 2*k, 2));

Crossrefs

Cf. A009153, A024430, A357650.

Cf. A356572.

Sequence in context: A143631 A083328 A000846 * A231822 A049684 A037540

Adjacent sequences: A357646 A357647 A357648 * A357650 A357651 A357652

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2022

Status

approved