A383203 Expansion of e.g.f. f(x) * exp(f(x)), where f(x) = (exp(2*x) - 1)/2.

0, 1, 4, 19, 104, 641, 4380, 32803, 266768, 2337505, 21925236, 218946003, 2316939256, 25878593313, 304020964876, 3745210267939, 48248600421664, 648460085178689, 9072650530778084, 131884007007981075, 1988341404357799048, 31040812899065995073, 501049583881525932028

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=1..n} k * 2^(n-k) * Stirling2(n,k).

Mathematica

Table[Sum[k*2^(n - k)*StirlingS2[n, k], {k, n}], {n, 0, 25}] (* Wesley Ivan Hurt, Feb 06 2026 *)

Prog

(PARI) a(n) = sum(k=1, n, k*2^(n-k)*stirling(n, k, 2));

Crossrefs

Column k=1 of A154602.

Sequence in context: A186997 A367239 A062265 * A088129 A369109 A082030

Adjacent sequences: A383200 A383201 A383202 * A383204 A383205 A383206

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2025

Status

approved