A336228 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k).

1, 1, 6, 75, 1684, 59005, 2977566, 204512875, 18346977608, 2083115635065, 291996210173410, 49525220811387871, 9996609976117991436, 2368117724291275331869, 650613686811158069472942, 205196311013650099853516115, 73633144885479474283911225616

Offset: 0

Author

Ilya Gutkovskiy, Jul 12 2020

Keywords

• nonn

Crossrefs

Cf. A006153, A102221.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[1/(1 - Sqrt[x] BesselI[1, 2 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

Formula

a(n) = (n!)^2 * [x^n] 1 / (1 - sqrt(x) * BesselI(1,2*sqrt(x))).