A351151 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).

1, 0, 1, 5, 26, 145, 901, 6420, 52501, 480955, 4795626, 51066375, 576182001, 6879462680, 86955722401, 1162559359745, 16392133866026, 242734091500445, 3758825675820501, 60660434188558780, 1017770666417312501, 17725289455315892375, 320047193447632729626

Offset: 0

Author

Ilya Gutkovskiy, Feb 02 2022

Keywords

• nonn

Comments

Shifts 2 places left under 5th-order binomial transform.

Crossrefs

Cf. A000994, A005011, A351056, A351143, A351144, A351150, A351152.

Programs

Mathematica

nmax = 22; A[] = 0; Do[A[x] = 1 + x^2 A[x/(1 - 5 x)]/(1 - 5 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[Binomial[n - 2, k] 5^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 5^k * a(n-k-2).