OFFSET
0,3
COMMENTS
Sum_{n>=0} a(n)/n!^3 = exp(zeta(3)) = 3.326953110002499790...
FORMULA
a(0) = 1; a(n) = (n-1)! * (n!)^2 * Sum_{k=0..n-1} a(k) / ((k!)^3 * (n-k)^2). - Ilya Gutkovskiy, Jul 18 2020
EXAMPLE
A(x) = 1 + x + 5*x^2/2!^3 + 71*x^3/3!^3 + 2276*x^4/4!^3 +...
where
log(A(x)) = x + x^2/8 + x^3/27 + x^4/64 + x^5/125 + x^6/216 +...
PROG
(PARI) {a(n)=n!^3*polcoeff(exp(sum(m=1, n, x^m/m^3)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 25 2011
STATUS
approved