OFFSET
0,2
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (1 - 3*x).
a(0) = 1; a(n) = 3 * n^2 * a(n-1) + 1.
MATHEMATICA
Table[n!^2 Sum[3^(n - k)/k!^2, {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 3 x), {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 27 2021
STATUS
approved