A352357 Expansion of e.g.f. 1/(1 - Sum_{k>=1} binomial(k+2,3) * x^k/k!).
1, 1, 6, 40, 364, 4155, 56836, 907158, 16547896, 339587445, 7743161740, 194212763756, 5314051343932, 157520046898695, 5028409083962824, 171984217743856890, 6274444932921616176, 243215342466576246185, 9982290554423689511124, 432464578359391409082952
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(x+x^2+x^3/6)*exp(x)))) -
PARI
a(n) = if(n==0, 1, sum(k=1, n, binomial(k+2, 3)*binomial(n, k)*a(n-k)));
Formula
E.g.f.: 1/(1 - (x + x^2 + x^3/6)*exp(x)).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(k+2,3) * binomial(n,k) * a(n-k).