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%I #11 Jul 19 2016 10:57:48
%S 1,2,7,26,109,466,2142,9870,47438,228750,1133373,5618252,28431660,
%T 143809690,738803296,3794224624,19718366257,102416655624,537315418006,
%U 2816334685644,14883569577907,78603101910486,417974689553235,2220832056696030,11871111721797874
%N G.f. satisfies: A(x) = Product_{n>=0} 1/(1-a(n)*x^(n+1))^2 = Sum_{n>=0} a(n)*x^n.
%C Equals the self-convolution of A093639.
%H Vaclav Kotesovec, <a href="/A093638/b093638.txt">Table of n, a(n) for n = 0..184</a>
%F G.f. satisfies: A(x) = exp( 2*Sum_{n>=1} Sum_{k>=1} a(k)^n * (x^k)^n /n ) = Sum_{n>=0} a(n)*x^n. - _Paul D. Hanna_, Feb 13 2013
%e G.f.: A(x) = 1 + 2*x + 7*x^2 + 26*x^3 + 109*x^4 + 466*x^5 + 2142*x^6 +...
%e where
%e A(x) = 1/((1-x)*(1-2*x^2)*(1-7*x^3)*(1-26*x^4)*(1-109*x^4)*(1-466*x^4)*...)^2.
%o (PARI) a(n)=polcoeff(prod(i=0,n-1,1/(1-a(i)*x^(i+1))^2)+x*O(x^n),n)
%o (PARI) a(n)=local(A=1+x); for(i=1, n, A=exp(2*sum(m=1, n, 1/m*sum(k=1, n, polcoeff(A+O(x^k), k-1)^m*x^(m*k)) +x*O(x^n)))); polcoeff(A, n)
%o for(n=0,30,print1(a(n),", ")) \\ _Paul D. Hanna_, Feb 13 2013
%Y Cf. A093637, A093639.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 07 2004
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