A357617 Expansion of e.g.f. sinh( (exp(4*x) - 1)/4 ).

0, 1, 4, 17, 88, 657, 6844, 83393, 1072880, 14242785, 197046964, 2895895345, 45930435016, 789930042865, 14628150636012, 287915593953889, 5950831121362656, 128180962018224833, 2868724306984850020, 66704877850797014353, 1613138176448134032440

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-2*k) * Stirling2(n,2*k+1).

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[Sinh[(Exp[4*x] - 1)/4], {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(4*x)-1)/4))))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^(n-1-2*k)*stirling(n, 2*k+1, 2));

Crossrefs

Cf. A009599, A024429, A356572.

Cf. A357650.

Sequence in context: A135168 A364212 A354308 * A350474 A058279 A143405

Adjacent sequences: A357614 A357615 A357616 * A357618 A357619 A357620

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2022

Status

approved