A351132 G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).

0, 1, 0, 1, 10, 76, 530, 3701, 27810, 237151, 2316350, 25135126, 292106400, 3559029501, 45211131460, 600619791201, 8384107777030, 123237338584576, 1904128564485610, 30789744821412401, 518479182191232950, 9057086806410632751, 163745788914416588050

Offset: 0

Author

Ilya Gutkovskiy, Feb 03 2022

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000995, A005011, A351028, A351053, A351056, A351128, A351151, A351161.

Programs

Mathematica

nmax = 22; A[] = 0; Do[A[x] = x + x^2 A[x/(1 - 5 x)]/(1 - 5 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[1] = 1; 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) = 0, a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 5^k * a(n-k-2).