A370508 - OEIS

%I #14 Feb 20 2024 13:47:00

%S 1,1,2,6,23,116,702,4944,39722,358578,3593664,39595440,475746474,

%T 6190838544,86740334160,1301939398080,20842001737224,354469125185880,

%U 6382790173842480,121310821042966800,2426863248540057480,50975836645480342560,1121691979824460425360

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1-x^3))^k))

%o (PARI) a(n) = sum(k=0, n\4, (-1)^k*(n-3*k)!*binomial(n-3*k, k));

%Y Cf. A013999, A212580.

%Y Cf. A370510.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Feb 20 2024