A336227 a(0) = 1; a(n) = n * Sum_{k=0..n-1} binomial(n-1,k)^2 * a(k).

1, 1, 4, 27, 292, 4425, 89106, 2280901, 71928872, 2728450017, 122145511510, 6354868381521, 379376236939404, 25710543779239501, 1960001963705060926, 166753195643254805565, 15724259680648667902096, 1633462474351643785483457, 185931510605274506452763166

Offset: 0

Author

Ilya Gutkovskiy, Jul 12 2020

Keywords

• nonn

Crossrefs

Cf. A000248, A023998.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = n Sum[Binomial[n - 1, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[Sqrt[x] BesselI[1, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2

Formula

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