A351757 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 3*x)) / (1 - 3*x)^2.

1, 1, 7, 43, 289, 2239, 19699, 192025, 2042971, 23520715, 291099349, 3849621019, 54110928355, 804827487493, 12619011606775, 207885167529523, 3587864566792753, 64705561315720135, 1216574535057705979, 23797327657083197113, 483390249416359706995

Offset: 0

Author

Ilya Gutkovskiy, Feb 18 2022

Keywords

• nonn

Crossrefs

Cf. A004212, A040027, A255927, A351756.

Programs

Mathematica

nmax = 20; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 3 x)]/(1 - 3 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Formula

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