A351815 G.f. A(x) satisfies A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x).

1, 1, 2, 9, 53, 386, 3422, 35300, 412084, 5364255, 76952267, 1203835714, 20362911276, 369906504888, 7175947738672, 147944905766929, 3227970924123268, 74264452788294013, 1795825803391367571, 45514495928632484735, 1205981001167335524448, 33331235326744168532151

Offset: 0

Author

Ilya Gutkovskiy, Feb 20 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..452

Crossrefs

Cf. A000110, A125273, A351813, A351814.

Programs

Mathematica

nmax = 21; A[] = 0; Do[A[x] = 1 + x A[x/(1 - x)^5]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 4 k - 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+4*k-1,n-k-1) * a(k).