A373759 Expansion of e.g.f. exp(x^4/(24 * (1 - x)^3)).

1, 0, 0, 0, 1, 15, 180, 2100, 25235, 319410, 4299750, 61815600, 950524575, 15633092475, 274749725250, 5151569172750, 102831791687625, 2179782464359500, 48933251188321500, 1160002995644493000, 28956069155772383625, 759014081927743516875

Offset

0,6

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-k-1,n-4*k)/(24^k * k!).

a(0) = 1; a(n) = ((n-1)!/24) * Sum_{k=4..n} k * binomial(k-2,k-4) * a(n-k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\4, binomial(n-k-1, n-4*k)/(24^k*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=4, i, j*binomial(j-2, j-4)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A361545, A361577, A373758.

Sequence in context: A004992 A055084 A005461 * A138443 A235455 A016158

Adjacent sequences: A373756 A373757 A373758 * A373760 A373761 A373762

Keyword

nonn

Author

Seiichi Manyama, Jun 17 2024

Status

approved