A370510 - OEIS

%I #14 Feb 20 2024 13:48:04

%S 1,1,2,6,25,124,738,5136,40922,367218,3664224,40240560,482278326,

%T 6263414736,87618506160,1313435465280,21003904630824,356910121855320,

%U 6422020465846320,121980351190294800,2438956634267865720,51206322309647263200,1126314497201852150640

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

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

%Y Cf. A240172, A370509.

%Y Cf. A370508.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Feb 20 2024