A343975 a(0) = 1; a(n) = 3 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 3, 15, 81, 489, 3237, 23211, 178707, 1467051, 12768345, 117263829, 1131901521, 11444383251, 120847326879, 1329303053391, 15197269729689, 180211641841353, 2212525627591533, 28078380387448515, 367782119667874083, 4965441830591976339, 69014083524412401873, 986364827548578356421

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A027710, A032033, A040027, A078940, A343523, A344735, A344840, A345077, A345078, A345081.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 3 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 22}]
nmax = 22; A[] = 0; Do[A[x] = 1 + 3 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 + 3 * x * A(x/(1 - x)) / (1 - x)^2.