OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: A(x) = Product_{n>=1} 1/(1 - x^n)^A074206(n) where A074206(n) equals the number of ordered factorizations of n.
a(n) ~ exp((1 + 1/r) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(1+r)) * n^(r/(1+r))) * (-Gamma(1+r) * Zeta(1+r) / Zeta'(r))^(1/(10*(1+r))) / ((2*Pi)^(29/50) * sqrt(1+r) * n^((6 + 5*r)/(10*(1+r)))), where r = A107311 = 1.7286472389981836181351... is the root of the equation Zeta(r) = 2, Zeta'(r) = -1/A247667. - Vaclav Kotesovec, Nov 04 2018
PROG
(PARI) {a(n)=local(A=1+x); for(i=2, n, A=1/(1-x)*prod(n=2, i, subst(A, x, x^n+x*O(x^i)))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 12 2007
STATUS
approved