A367875 Expansion of e.g.f. exp(x * (3 + exp(x))).

1, 4, 18, 91, 512, 3169, 21352, 155257, 1209680, 10039825, 88318136, 819958033, 8004898600, 81913041721, 876117919616, 9770201709649, 113347591376672, 1365288066794017, 17043527322085096, 220145837754233713, 2937871757773069496, 40451715334029650953

Offset

0,2

Links

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

Formula

G.f.: Sum_{k>=0} x^k / (1 - (k+3)*x)^(k+1).

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

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

Crossrefs

Cf. A000248, A080108, A367874.

Cf. A245834.

Sequence in context: A355247 A269450 A206639 * A172964 A317135 A196150

Adjacent sequences: A367872 A367873 A367874 * A367876 A367877 A367878

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 03 2023

Status

approved