A368576 a(n) = n! * Sum_{k=0..n} binomial(k+4,5) / k!.

0, 1, 8, 45, 236, 1306, 8088, 57078, 457416, 4118031, 41182312, 453008435, 5436105588, 70669378832, 989371312216, 14840569694868, 237449115133392, 4036634957288013, 72659429231210568, 1380529155393034441, 27610583107860731324, 579822245265075410934

Offset

0,3

Links

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

Formula

a(0) = 0; a(n) = n*a(n-1) + binomial(n+4,5).

E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1-x).

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1-x))))

Crossrefs

Cf. A007526, A103519, A368574, A368575.

Cf. A000389.

Sequence in context: A297089 A032208 A163003 * A055422 A204618 A289896

Adjacent sequences: A368573 A368574 A368575 * A368577 A368578 A368579

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 31 2023

Status

approved