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