A352468 a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k)^3 * a(n-k).

1, 1, 217, 735751, 16225658905, 1485378967457251, 429009059656530602767, 324779065084721999818137709, 563805297587600177760431368896025, 2028620600892240327820781003315525267467, 13978450121866685445815888094629703793828769467

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2022

Keywords

• nonn

Crossrefs

Cf. A094088, A336195, A352467, A352471.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n, 2 k]^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 10}]
nmax = 20; Take[CoefficientList[Series[1/(1 - Sum[x^(2 k)/(2 k)!^3, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3, {1,-1, 2}]

Formula

Sum_{n>=0} a(n) * x^(2*n) / (2*n)!^3 = 1 / (1 - Sum_{n>=1} x^(2*n) / (2*n)!^3).