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%I #10 Aug 15 2012 00:37:45
%S 1,3,21,244,4056,88770,2426553,79893084,3085719033,137035475333,
%T 6888543200172,387050951446488,24058512516152880,1640162160152393778,
%U 121746052707050425113,9778208522585460239036,845181303653928350311539,78247854362736258482850285
%N G.f.: 1 = Sum_{n>=0} a(n)*x^n / Product_{k=1..n+1} (1+k*x)^3.
%C Compare to the g.f. for factorials: 1 = Sum_{n>=0} n!*x^n/Product_{k=1..n+1} (1+k*x).
%e 1 = 1/(1+x)^3 + 3*x/((1+x)^3*(1+2*x)^3) + 21*x^2/((1+x)^3*(1+2*x)^3*(1+3*x)^3) + 244*x^3/((1+x)^3*(1+2*x)^3*(1+3*x)^3*(1+4*x)^3) +...
%o (PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k/prod(j=1, k+1, 1+j*x+x*O(x^n))^3), n))}
%Y Cf. A118804, A215529.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 23 2011
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