A368271 Expansion of e.g.f. exp(2*x) / (1 + x*exp(x)).

1, 1, 0, -1, 4, 7, -74, 23, 2136, -7345, -77006, 712879, 2499124, -69799897, 88342398, 7311735143, -50617554896, -762825930977, 12821702643946, 56041362405119, -2956159258069044, 8447845572175031, 660257137187089270, -7376306690095890185

Offset: 0

Author

Seiichi Manyama, Dec 19 2023

Keywords

• sign
• easy

Crossrefs

Cf. A302397, A368272, A368273.

Cf. A368265, A368267.

Programs

PARI

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

Formula

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