A344735 a(0) = 1; a(n) = 4 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 4, 24, 156, 1120, 8740, 73384, 657900, 6259184, 62876852, 664134968, 7349666684, 84956020864, 1023006054980, 12802727760840, 166174971580684, 2232866214809360, 31007771007956948, 444360490882720344, 6562410784684023452, 99749853821538893216, 1558780425524233360740

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A040027, A078944, A078945, A094417, A343523, A343975, A344840, A345077, A345078, A345081.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 4 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 21}]
nmax = 21; A[] = 0; Do[A[x] = 1 + 4 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 + 4 * x * A(x/(1 - x)) / (1 - x)^2.