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O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + k*(k+1)*(k+2)/6*x).
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%I #4 Mar 30 2012 18:37:01

%S 1,1,2,6,20,90,465,2826,20020,158348,1430189,14217275,157279196,

%T 1903617880,25151383277,361228405394,5594555181227,93472423847492,

%U 1671138501448565,31988293954710201,651665490924639449

%N O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + k*(k+1)*(k+2)/6*x).

%e A(x) = 1 + x*(1+x) + x^2*(1+x)*(1+4x) + x^3*(1+x)*(1+4x)*(1+10x) +...

%o (PARI) a(n)=polcoeff(sum(k=0,n,x^k*prod(j=0,k,1+j*(j+1)*(j+2)/3!*x+x*O(x^n))),n)

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 28 2006