%I #7 Oct 28 2014 17:52:55
%S 1,1,3,17,86,674,5604,55236,579648,7302816,95738400,1391181120,
%T 21792119040,366215610240,6581045197440,126809720795520,
%U 2559529594782720,54828458042158080,1242024477363855360,29351942535941867520,729546143909048524800
%N E.g.f.: Sum_{n>=0} Product_{k=1..n} -log(1-x^k)/(1-x^k).
%H Vaclav Kotesovec, <a href="/A203851/b203851.txt">Table of n, a(n) for n = 0..250</a>
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 17*x^3/3! + 86*x^4/4! + 674*x^5/5! +...
%e where
%e A(x) = 1 - log(1-x)/(1-x) + log(1-x)*log(1-x^2)/((1-x)*(1-x^2)) - log(1-x)*log(1-x^2)*log(1-x^3)/((1-x)*(1-x^2)*(1-x^3)) +...
%o (PARI) {a(n)=n!*polcoeff(1+sum(m=1, n, prod(k=1, m, -log(1-x^k +x*O(x^n))/(1-x^k) ) ), n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 29 2012