%I #6 Feb 20 2022 06:46:17

%S 1,1,11,101,971,10621,133251,1872261,28840251,481539021,8658919571,

%T 166768522101,3421884596011,74443313899901,1710104876681571,

%U 41338914172638021,1048412294411955451,27821558652073329261,770663280948805164051,22235353608667471453621

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

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

%t 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]

%t 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}]

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 19 2022