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