A351792 Expansion of e.g.f. 1/(1 - x*exp(-3*x)).

1, 1, -4, -3, 132, -375, -8298, 86121, 636696, -20318607, 15154290, 5555366289, -57903946092, -1608939709767, 44662076643870, 329040381072825, -31446740971136592, 195779189199531105, 21694625692807192938, -496937940680594097279

Offset: 0

Author

Seiichi Manyama, Feb 19 2022

Keywords

• sign

Crossrefs

Column k=3 of A351791.

Cf. A336951, A351778.

Programs

Mathematica

a[0] = 1; a[n_] := n!*Sum[(-3*(n - k))^k/k!, {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 19 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(-3*x))))

PARI

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

PARI

a(n) = if(n==0, 1, n*sum(k=0, n-1, (-3)^(n-1-k)*binomial(n-1, k)*a(k)));

Formula

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

a(0) = 1 and a(n) = n * Sum_{k=0..n-1} (-3)^(n-1-k) * binomial(n-1,k) * a(k) for n > 0.