A345077 a(0) = 1; a(n) = 6 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 6, 48, 414, 3876, 38946, 416808, 4722774, 56379756, 706236426, 9250945008, 126342991614, 1794459834036, 26445918969906, 403610795535288, 6367606516836774, 103683034842399996, 1739933892930544986, 30052751213767045248, 533635421576480845134, 9730601644306627161156

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A040027, A094419, A144223, A343523, A343975, A344735, A344840, A345078, A345081.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 6 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 20}]
nmax = 20; A[] = 0; Do[A[x] = 1 + 6 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 + 6 * x * A(x/(1 - x)) / (1 - x)^2.