OFFSET
0,4
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x ).
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=2} x^n / n^2 ).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 2, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 13 2021
STATUS
approved