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

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A006153, A072597, A092148, A368265.

Sequence in context: A370415 A113112 A278578 * A338681 A069740 A173008

Adjacent sequences: A368263 A368264 A368265 * A368267 A368268 A368269

Keyword

sign,easy,changed

Author

Seiichi Manyama, Dec 19 2023

Status

approved