A345081 a(0) = 1; a(n) = 8 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 8, 80, 856, 9824, 119912, 1547376, 21007992, 298874496, 4440618120, 68706037904, 1104224971416, 18394192882336, 316974497161384, 5640790811468976, 103503851543959224, 1955546066369814208, 37994858794236710088, 758272809049577019600, 15527828509092566876888

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A040027, A221159, A238465, A343523, A343975, A344735, A344840, A345077, A345078.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 8 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; A[] = 0; Do[A[x] = 1 + 8 x A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 + 8 * x * A(x/(1 - x)) / (1 - x)^2.