A368273 Expansion of e.g.f. exp(-2*x) / (1 + x*exp(x)).

1, -3, 8, -17, 20, 23, -50, -1185, 6648, 20143, -372646, 179111, 25378468, -126050121, -1849977930, 23353880527, 109161798512, -3986970251809, 6487865966386, 680166849412311, -5885809282265124, -109572316727641433, 2250978116175344846, 11909910338327490623

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[-2x]/(1+x Exp[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 23 2025 *)

Prog

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

Crossrefs

Cf. A302397, A368271, A368272.

Sequence in context: A079666 A193684 A308850 * A335047 A048230 A294412

Adjacent sequences: A368270 A368271 A368272 * A368274 A368275 A368276

Keyword

sign

Author

Seiichi Manyama, Dec 19 2023

Status

approved