A379993 Expansion of e.g.f. 1/(1 - x * exp(x))^4.

1, 4, 28, 252, 2776, 35940, 533304, 8908228, 165247072, 3368072196, 74782987240, 1796037420804, 46379441090448, 1281203788073092, 37694510810334616, 1176606639075726660, 38833052393329645504, 1351066066253778043908, 49417629820950190273992

Offset: 0

Author

Seiichi Manyama, Jan 07 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A379943, A379994, A379995, A379996.

Cf. A006153, A377529, A377530.

Programs

Mathematica

nmax=18;CoefficientList[Series[1/(1 - x * Exp[x])^4,{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 05 2025 *)

PARI

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+3, 3)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+3,3)/(n-k)!.

a(n) == 0 (mod 4) for n>0.