OFFSET
0,3
COMMENTS
Compare to: exp( Sum_{n>=1} (exp(x) - 1)^n/n ) = 1/(2-exp(x)), the e.g.f. of Fubini numbers (A000670).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ c * d^n * (n!)^2 / n^(3/2), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491..., r = 0.873702433239668330496568304720719298... is the root of the equation exp(1/r)/r + (1+exp(1/r)) * LambertW(-exp(-1/r)/r) = 0, and c = 0.37498840921734807101035131780130551... . - Vaclav Kotesovec, Aug 21 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + 6*x^2/2! + 95*x^3/3! + 3043*x^4/4! + 167342*x^5/5! +...
PROG
(PARI) {a(n) = n!*polcoeff( exp( sum(m=1, n+1, (exp(m*x +x*O(x^n)) - 1)^m / m) ), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 21 2014
STATUS
approved