A367874 Expansion of e.g.f. exp(x * (2 + exp(x))).

1, 3, 11, 48, 241, 1358, 8445, 57256, 419233, 3290202, 27507349, 243731084, 2278919697, 22402234390, 230781192301, 2484462888312, 27880896280513, 325432611292082, 3943062342781605, 49504837209940612, 642982531293731761, 8626753575445207278

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: Sum_{k>=0} x^k / (1 - (k+2)*x)^(k+1).

a(n) = Sum_{k=0..n} (k+2)^(n-k) * binomial(n,k).

a(0) = 1; a(n) = 2 * a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * k * a(n-k). - Ilya Gutkovskiy, Feb 02 2024

Prog

(PARI) a(n) = sum(k=0, n, (k+2)^(n-k)*binomial(n, k));

Crossrefs

Cf. A000248, A080108, A367875.

Cf. A240165.

Sequence in context: A233162 A345341 A186185 * A317170 A127087 A113060

Adjacent sequences: A367871 A367872 A367873 * A367875 A367876 A367877

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 03 2023

Status

approved