A377582 Expansion of e.g.f. (1 + x * exp(x))^3.

1, 3, 12, 51, 228, 1035, 4698, 21063, 92424, 395091, 1643790, 6664383, 26387100, 102286587, 389125506, 1455994935, 5368721808, 19541252259, 70312410774, 250408115823, 883617559140, 3092276105163, 10740749281482, 37053754521831, 127037475064728, 433073722098675

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

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

G.f.: (1-17*x+127*x^2-542*x^3+1453*x^4-2543*x^5+2973*x^6-2478*x^7+1626*x^8-648*x^9) / ((1-x)^2*(1-2*x)^3*(1-3*x)^4).

Prog

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

Crossrefs

Cf. A002999, A377583.

Cf. A001815, A052791.

Cf. A377530, A377575.

Sequence in context: A151317 A151184 A256334 * A151185 A151186 A151187

Adjacent sequences: A377579 A377580 A377581 * A377583 A377584 A377585

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 02 2024

Status

approved