A344840 a(0) = 1; a(n) = 5 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 5, 35, 265, 2195, 19625, 187755, 1909185, 20521515, 232124745, 2752591475, 34108980105, 440444019835, 5912197332865, 82320781521195, 1186703083508025, 17680850448587155, 271845880552898985, 4307188044378111915, 70236616096770062945, 1177406236243423738475

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A040027, A094418, A144180, A343523, A343975, A344735, A345077, A345078, A345081.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 5 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 20}]
nmax = 20; A[] = 0; Do[A[x] = 1 + 5 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 + 5 * x * A(x/(1 - x)) / (1 - x)^2.