A351811 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.

1, 1, 11, 101, 971, 10621, 133251, 1872261, 28840251, 481539021, 8658919571, 166768522101, 3421884596011, 74443313899901, 1710104876681571, 41338914172638021, 1048412294411955451, 27821558652073329261, 770663280948805164051, 22235353608667471453621

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Mathematica

nmax = 19; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 5 x)]/(1 - 5 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] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A005011, A040027, A351756, A351757, A351810, A351812.

Sequence in context: A122105 A332853 A289850 * A171750 A191420 A118937

Adjacent sequences: A351808 A351809 A351810 * A351812 A351813 A351814

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2022

Status

approved