A368768 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+3,4) / k!).

1, 0, 5, 0, 35, 105, 756, 5082, 40986, 368379, 3684505, 40528554, 486344013, 6322470349, 88514587266, 1327718805930, 21243500898756, 361139515274007, 6500511274938111, 123509714223816794, 2470194284476344735, 51874079974003228809, 1141229759428071046448

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = n*a(n-1) + (-1)^n * binomial(n+3,4).

a(n) = n! + (-1)^n * A368586(n).

E.g.f.: (1 - x * (1-3*x/2+x^2/2-x^3/24) * exp(-x)) / (1-x).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 3, binomial(3, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))

Crossrefs

Cf. A368765, A368766, A368767.

Cf. A368586, A368764.

Sequence in context: A186746 A208928 A348209 * A297206 A373388 A103709

Adjacent sequences: A368765 A368766 A368767 * A368769 A368770 A368771

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2024

Status

approved