A351151 - OEIS

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

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OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for 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).

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}]