A351816 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x)^3.

1, 1, 4, 16, 83, 526, 3826, 31338, 285556, 2857831, 31083421, 364523891, 4579906098, 61313286380, 870531542926, 13055593578453, 206097824225131, 3414146518958089, 59189048364709453, 1071264611091540458, 20197719805598878119, 395917304689782855768

Offset: 0

Author

Ilya Gutkovskiy, Feb 20 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..486

Crossrefs

Cf. A000110, A045501, A125274, A351813, A351817, A351818.

Programs

Mathematica

nmax = 21; A[] = 0; Do[A[x] = 1 + x A[x/(1 - x)^3]/(1 - x)^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 2 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+2*k+1,n-k-1) * a(k).