OFFSET
0,3
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = (1 - BesselJ(0,2*sqrt(x))) / (1 - x).
a(0) = 0; a(n) = n^2 * a(n-1) - (-1)^n.
MATHEMATICA
Table[n!^2 Sum[(-1)^(k + 1)/k!^2, {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[(1 - BesselJ[0, 2 Sqrt[x]])/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 23 2021
STATUS
approved