A368763 a(n) = n! * (1 + Sum_{k=0..n} binomial(k+2,3) / k!).

1, 2, 8, 34, 156, 815, 4946, 34706, 277768, 2500077, 25000990, 275011176, 3300134476, 42901748643, 600624481562, 9009367224110, 144149875586576, 2450547884972761, 44109861929510838, 838087376660707252, 16761747533214146580, 351996698197497079951

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = n*a(n-1) + binomial(n+2,3).

a(n) = n! + A368574(n).

E.g.f.: (1 + x * (1+x+x^2/6) * exp(x)) / (1-x).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x))/(1-x)))

Crossrefs

Cf. A033540, A368762, A368764.

Cf. A368574, A368767.

Sequence in context: A150895 A150896 A150897 * A150898 A150899 A150900

Adjacent sequences: A368760 A368761 A368762 * A368764 A368765 A368766

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2024

Status

approved