A357650 Expansion of e.g.f. cosh( (exp(4*x) - 1)/4 ).

1, 0, 1, 12, 113, 1000, 8977, 86996, 959905, 12303888, 179038689, 2840696540, 47684181393, 835731314808, 15277172343409, 292597596283684, 5900038421042753, 125488177929542944, 2809541905807203009, 65903118624174027436, 1610968753088423886257

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/2)} 4^(n-2*k) * Stirling2(n,2*k).

a(n) ~ 2^(2*n-1) * exp(n/LambertW(4*n) - n - 1/4) * n^n / (LambertW(4*n)^n * sqrt(1 + LambertW(4*n))). - Vaclav Kotesovec, Oct 07 2022

Mathematica

With[{m = 20}, Range[0, m]! * CoefficientList[Series[Cosh[(Exp[4*x] - 1)/4], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh((exp(4*x)-1)/4)))
(PARI) a(n) = sum(k=0, n\2, 4^(n-2*k)*stirling(n, 2*k, 2));

Crossrefs

Cf. A009153, A024430, A357649.

Cf. A357617.

Sequence in context: A083767 A285154 A153882 * A322649 A198375 A124651

Adjacent sequences: A357647 A357648 A357649 * A357651 A357652 A357653

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2022

Status

approved