%I #4 Mar 30 2012 18:37:01
%S 1,1,2,5,14,48,181,772,3620,18511,102869,613584,3926895,26734671,
%T 193310243,1477081245,11896869336,100700815331,893438783126,
%U 8291513009130,80302486087937,810290260679230,8502192961792190
%N O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + k*(k+1)/2*x).
%e A(x) = 1 + x*(1+x) + x^2*(1+x)*(1+3x) + x^3*(1+x)*(1+3x)*(1+6x) +...
%o (PARI) a(n)=polcoeff(sum(k=0,n,x^k*prod(j=0,k,1+j*(j+1)/2*x+x*O(x^n))),n)
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 28 2006
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