OFFSET
0,3
FORMULA
a(n) = (n!)^2 * [x^n] 1 / (1 - sqrt(x) * BesselI(1,2*sqrt(x))).
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 12 2020
STATUS
approved