A352863 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+3,k+3) * a(k).

1, 4, 30, 260, 2625, 30296, 393372, 5675160, 90062775, 1559197420, 29242803018, 590638256572, 12781663255725, 295040675093360, 7236113219901240, 187911083837928048, 5150869386839932995, 148622674413214927140, 4502761102131604279590, 142914444471765753144820

Offset: 0

Author

Ilya Gutkovskiy, Apr 06 2022

Keywords

• nonn

Crossrefs

Cf. A000292, A000670, A045499, A052882, A105480, A154931, A240798.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 3, k + 3] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[D[x^3/(3! (2 - Exp[x])), {x, 3}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: d^3/dx^3 ( x^3 / (3!*(2 - exp(x))) ).

a(n) = A000292(n+1) * A000670(n).