A352466 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(2*n,2*k)^3 * k * a(n-k).

1, 1, 109, 124876, 704029453, 13294133177626, 665514245564815384, 75462508236267111825685, 17305487139219914670764064013, 7368678746697280907127091048286734, 5449131877967324738667220718996986592734, 6632563741264033978048120096103173533343094035

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2022

Keywords

• nonn

Crossrefs

Cf. A005046, A061684, A352465, A352469.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[2 n, 2 k]^3 k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 11}]
nmax = 22; Take[CoefficientList[Series[Exp[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 = exp( Sum_{n>=1} x^(2*n) / (2*n)!^3 ).