A370508 Expansion of Sum_{k>=0} k! * ( x * (1-x^3) )^k.

1, 1, 2, 6, 23, 116, 702, 4944, 39722, 358578, 3593664, 39595440, 475746474, 6190838544, 86740334160, 1301939398080, 20842001737224, 354469125185880, 6382790173842480, 121310821042966800, 2426863248540057480, 50975836645480342560, 1121691979824460425360

Offset: 0

Author

Seiichi Manyama, Feb 20 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A013999, A212580.

Cf. A370510.

Programs

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\4, (-1)^k*(n-3*k)!*binomial(n-3*k, k));

Formula

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