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%I #9 Nov 03 2014 02:50:34
%S 1,1,5,43,503,7395,130417,2677347,62652163,1645424927,47918249503,
%T 1532532861117,53400906126039,2013774998655263,81717093507007097,
%U 3550624402561500703,164477470918884953215,8092070874197301949727,421396510870277400155719
%N G.f.: sqrt( Sum_{n>=0} x^n * Product_{k=1..n} (2*k - x) / (1 - 2*k*x) ).
%C Limit n->infinity A231229(n) / A231277(n) = 2. - _Vaclav Kotesovec_, Nov 02 2014
%H Vaclav Kotesovec, <a href="/A231277/b231277.txt">Table of n, a(n) for n = 0..235</a>
%F Self-convolution yields A231229.
%F a(n) ~ 2^(n-2) * n! / (log(2))^(n+1). - _Vaclav Kotesovec_, Nov 02 2014
%e A(x) = 1 + x + 5*x^2 + 43*x^3 + 503*x^4 + 7395*x^5 + 130417*x^6 +...
%e where
%e A(x)^2 = 1 + x*(2-x)/(1-2*x) + x^2*(2-x)*(4-x)/((1-2*x)*(1-4*x)) + x^3*(2-x)*(4-x)*(6-x)/((1-2*x)*(1-4*x)*(1-6*x)) + x^4*(2-x)*(4-x)*(6-x)*(8-x)/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)) +...
%o (PARI) {a(n)=polcoeff(sqrt(sum(m=0, n, x^m*prod(k=1, m, (2*k-x)/(1-2*k*x +x*O(x^n))))), n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A231229.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 06 2013
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