%I #2 Mar 30 2012 18:37:20
%S 1,1,4,38,693,21294,1011792,69920766,6710698740,862907887944,
%T 144436271624388,30735209866458888,8152133649148990080,
%U 2650418681465362135392,1041182371767985227729504
%N E.g.f.: A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=1..n} -log(1 - k(k+1)x/2).
%e E.g.f.: A(x) = 1 + x + 4x^2/2! + 38x^3/3! + 693x^4/4! + 21294x^5/5! +...
%e A(x) = 1 - log(1-x) + log(1-x)*log(1-3x)/2! - log(1-x)*log(1-3x)*log(1-6x)/3! +...
%o (PARI) {a(n)=n!*polcoeff(1+sum(j=1, n, (1/j!)*prod(k=1, j, -log(1-k*(k+1)/2*x +x*O(x^n)))), n)}
%Y Cf. A135751, A171778.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 18 2009