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%I #8 Aug 15 2012 00:40:45
%S 1,1,3,16,128,1396,19524,335676,6880388,164277924,4487230004,
%T 138213671308,4744574123684,179758555018740,7455418866550084,
%U 336136394342220156,16376124700916059428,857610538194682984548,48057661232590025818356,2869922852119148564815692
%N G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..n} (1 + k*x)^2.
%C Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x).
%e G.f.: 1/(1-x) = 1 + 1*x/(1+x)^2 + 3*x^2/((1+x)*(1+2*x))^2 + 16*x^3/((1+x)*(1+2*x)*(1+3*x))^2 + 128*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^2 +...
%o (PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, k, 1+j*x+x*O(x^n))^2), n))}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A118804, A215529.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 01 2012
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