A368291 Expansion of e.g.f. exp(x) / (1 - x*exp(2*x)).

1, 2, 9, 64, 601, 7046, 99169, 1628404, 30558609, 645145642, 15133509721, 390493864520, 10992015298345, 335198866337518, 11008101913855089, 387333950619801916, 14537422513124682913, 579719887191660443858, 24477810534426983873833

Offset: 0

Author

Seiichi Manyama, Dec 19 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A368292.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x]/(1-x Exp[2x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 27 2025 *)

PARI

a(n) = n!*sum(k=0, n, (2*(n-k)+1)^k/k!);

Formula

a(n) = n! * Sum_{k=0..n} (2*(n-k)+1)^k / k!.