OFFSET
0,3
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = 3 / (4 - BesselI(0,2*sqrt(3*x))).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 3^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[3/(4 - BesselI[0, 2 Sqrt[3 x]]), {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 25 2021
STATUS
approved