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%I #8 Oct 07 2012 00:15:38
%S 1,1,5,64,1577,64026,3887167,330394800,37487397201,5477556616750,
%T 1002201757761971,224502014115239136,60447250689539460925,
%U 19264011725572422723292,7172619686789755991626485
%N G.f. satisfies: A(x) = B(x*A(x)) where B(x) = Sum_{n>=0} x^n/n!^2 and A(x) = Sum_{n>=0} a(n)*x^n/n!^2.
%F G.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where A(x/B(x)) = B(x) = Sum_{n>=0} x^n/n!^2.
%F a(n) = [x^n/n!^2] B(x)^(n+1)/(n+1).
%e G.f.: A(x) = 1 + x + 5*x^2/2!^2 + 64*x^3/3!^2 + 1577*x^4/4!^2 +...
%e where A(x) = Sum_{n>=0} x^n*A(x)^n/n!^2.
%e Also, A(x/B(x)) = B(x) = 1 + x + x^2/2!^2 + x^3/3!^2 + x^4/4!^2 +...
%o (PARI) {a(n)=local(B=sum(m=0,n,x^m/m!^2+O(x^(n+2))));n!^2*polcoeff(serreverse(x/B)/x,n)}
%Y Cf. A217567.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 04 2011
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