OFFSET
0,3
COMMENTS
Sum_{n>=0} a(n)/n!^4 = exp(Pi^4/90) = 2.951528682853355...
FORMULA
a(0) = 1; a(n) = (n-1)! * (n!)^3 * Sum_{k=0..n-1} a(k) / ((k!)^4 * (n-k)^3). - Ilya Gutkovskiy, Jul 18 2020
EXAMPLE
A(x) = 1 + x + 9*x^2/2!^4 + 313*x^3/3!^4 + 30232*x^4/4!^4 + 6874776*x^5/5!^4 +...
where
log(A(x)) = x + x^2/2^4 + x^3/3^4 + x^4/4^4 + x^5/5^3 + x^6/6^4 +...
PROG
(PARI) {a(n)=n!^4*polcoeff(exp(sum(m=1, n, x^m/m^4)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 18 2012
STATUS
approved