A370511 Expansion of Sum_{k>=0} k! * ( x/(1-x^3) )^k.

1, 1, 2, 6, 25, 124, 738, 5137, 40926, 367236, 3664321, 40241168, 482282700, 6263450401, 87618831730, 1313438757210, 21003941166601, 356910563528412, 6422026243338846, 121980432505328545, 2438957859604373534, 51206341993873093608, 1126314833020691642497

Offset

0,3

Links

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

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x/(1-x^3))^k))
(PARI) a(n) = sum(k=0, n\3, (n-3*k)!*binomial(n-2*k-1, k));

Crossrefs

Cf. A001339, A276080.

Cf. A358493.

Sequence in context: A291558 A357902 A370510 * A074010 A352660 A349088

Adjacent sequences: A370508 A370509 A370510 * A370512 A370513 A370514

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 20 2024

Status

approved