OFFSET
0,3
FORMULA
a(n) = (n!)^2 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k*k!)).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[1/(1 - Sum[x^k/(k k!), {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^2
nmax = 16; Assuming[x > 0, CoefficientList[Series[1/(1 + EulerGamma - ExpIntegralEi[x] + Log[x]), {x, 0, nmax}], x]] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 13 2020
STATUS
approved