OFFSET
0,3
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^3 = -log(1 - Sum_{n>=1} x^n / n^3).
MATHEMATICA
a[0] = 0; a[n_] := a[n] = ((n - 1)!)^3 + (1/n) Sum[(Binomial[n, k] (n - k - 1)!)^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[-Log[1 - Sum[x^k/k^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 21 2020
STATUS
approved