A365794 Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(3/4).

1, 3, 27, 369, 6849, 160803, 4566987, 152204769, 5822610849, 251445000483, 12098060349147, 641736701136369, 37204969609266849, 2340437711290748163, 158770522442243864907, 11553653430580844747169, 897732793887437892390849, 74182365989862425679675843

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (2 - 1/2 * k/n) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 3*a(n-1) - 3*Sum_{k=1..n-1} (-2)^k * binomial(n-1,k) * a(n-k).

Mathematica

With[{nn=20}, CoefficientList[Series[1/(3-2Exp[2x])^(3/4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 30 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));

Crossrefs

Cf. A365777, A365782.

Sequence in context: A372201 A370288 A157089 * A138436 A141057 A365569

Adjacent sequences: A365791 A365792 A365793 * A365795 A365796 A365797

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2023

Status

approved