A373757 Expansion of e.g.f. exp(x^3/(6 * (1 - x)^2)).

1, 0, 0, 1, 8, 60, 490, 4480, 45920, 524440, 6619200, 91568400, 1377884200, 22401579200, 391192401600, 7300174281400, 144938169376000, 3049711320656000, 67777255079934400, 1586172656920051200, 38984454900431040000, 1003827897443395024000

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-k-1,n-3*k)/(6^k * k!).

a(0) = 1; a(n) = ((n-1)!/6) * Sum_{k=3..n} k * (k-2) * a(n-k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\3, binomial(n-k-1, n-3*k)/(6^k*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/6*sum(j=3, i, j*(j-2)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A361533, A361573.

Sequence in context: A129331 A369146 A005990 * A160228 A274746 A366216

Adjacent sequences: A373754 A373755 A373756 * A373758 A373759 A373760

Keyword

nonn

Author

Seiichi Manyama, Jun 17 2024

Status

approved