OFFSET
0,4
FORMULA
a(n) = (n!)^2 * [x^n] exp(-Sum_{k>=1} x^k / (k!)^2).
a(n) = (n!)^2 * [x^n] exp(1 - BesselI(0,2*sqrt(x))).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 20}]
nmax = 20; CoefficientList[Series[Exp[-Sum[x^k/(k!)^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jul 12 2020
STATUS
approved