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

Author

Seiichi Manyama, Mar 13 2022

Keywords

• nonn

Crossrefs

Cf. A006153, A308946, A352358.

Cf. A000292, A308862, A346889.

Programs

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).