A368266 Expansion of e.g.f. exp(-2*x) / (1 - x*exp(x)).

1, -1, 4, 1, 60, 393, 4498, 54689, 773384, 12268369, 216328614, 4195769433, 88776964444, 2034936319817, 50232646818890, 1328570248040497, 37481046375146640, 1123486426007081505, 35657224567565828302, 1194561018775753556777, 42125545306641497600036

Offset: 0

Author

Seiichi Manyama, Dec 19 2023

Keywords

• sign
• easy

Crossrefs

Cf. A006153, A072597, A092148, A368265.

Programs

Mathematica

CoefficientList[Series[Exp[-2*x]/ (1 - x*Exp[x]),{x,0,20}],x]Range[0,20]! (* Stefano Spezia, Feb 21 2025 *)

PARI

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

Formula

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