A365777 Expansion of e.g.f. (exp(2*x) / (2 - exp(2*x)))^(3/4).

1, 3, 15, 117, 1257, 17163, 284055, 5522877, 123344817, 3111071283, 87454712895, 2710961144037, 91862770847577, 3378032307195003, 133970268354806535, 5699864583381903597, 258956671286986317537, 12512342291081486212323, 640686944845321006836975

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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 * (1/2 * k/n - 2) * binomial(n,k) * a(n-k).

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

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. A124212, A276371.

Cf. A365794.

Sequence in context: A225109 A080290 A371984 * A372161 A369722 A259843

Adjacent sequences: A365774 A365775 A365776 * A365778 A365779 A365780

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2023

Status

approved