A370510 Expansion of Sum_{k>=0} k! * ( x * (1+x^3) )^k.
1, 1, 2, 6, 25, 124, 738, 5136, 40922, 367218, 3664224, 40240560, 482278326, 6263414736, 87618506160, 1313435465280, 21003904630824, 356910121855320, 6422020465846320, 121980351190294800, 2438956634267865720, 51206322309647263200, 1126314497201852150640
Offset: 0
Programs
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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, (n-3*k)!*binomial(n-3*k, k));
Formula
a(n) = Sum_{k=0..floor(n/4)} (n-3*k)! * binomial(n-3*k,k).