A377955 a(n) = n! * Sum_{k=0..n} binomial(k+3,n-k) / k!.

1, 4, 15, 58, 241, 1056, 4879, 23710, 120033, 635356, 3478351, 19796514, 115988305, 703052728, 4372581711, 28022140486, 183804777409, 1238244635700, 8520907808143, 60061024788106, 431735704061361, 3171780156493264, 23730347517489295, 181115025566445678

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f.: (1 + x)^3 * exp(x + x^2).

a(n) = -(n-5)*a(n-1) + 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.

Prog

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

Crossrefs

Cf. A018191, A047974, A377954, A377956.

Sequence in context: A160156 A102052 A128714 * A007342 A017951 A326212

Adjacent sequences: A377952 A377953 A377954 * A377956 A377957 A377958

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 12 2024

Status

approved