A356572 Expansion of e.g.f. sinh( (exp(3*x) - 1)/3 ).

0, 1, 3, 10, 45, 307, 2718, 26371, 265359, 2778976, 30916863, 372113623, 4873075056, 68908186765, 1037694932823, 16438615126282, 271972422548361, 4687666317874495, 84181305836224422, 1576083180118379527, 30757003280682603699, 624671260245315540568

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 3^(n-1-2*k) * Stirling2(n,2*k+1).

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[Sinh[(Exp[3*x] - 1)/3], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)

Prog

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

Crossrefs

Cf. A009599, A024429, A357617.

Cf. A357649.

Sequence in context: A000250 A118601 A005143 * A270493 A121138 A355050

Adjacent sequences: A356569 A356570 A356571 * A356573 A356574 A356575

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2022

Status

approved