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%I #7 Nov 02 2014 12:51:33
%S 1,1,2,6,23,106,565,3391,22523,163578,1286990,10886149,98377648,
%T 944863003,9602092037,102856190049,1157496371816,13644751751698,
%U 168052771354837,2157537327051316,28814062411243931,399551143081559391,5742819361050324227
%N G.f.: Sum_{n>=0} x^n*Product_{k=1..n} (1 - k*x) / (1 - (2*k)*x).
%H Vaclav Kotesovec, <a href="/A193321/b193321.txt">Table of n, a(n) for n = 0..270</a>
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 106*x^5 + 565*x^6 +...
%e where
%e A(x) = 1 + x*(1-x)/(1-2*x) + x^2*(1-x)*(1-2*x)/((1-2*x)*(1-4*x)) + x^3*(1-x)*(1-2*x)*(1-3*x)/((1-2*x)*(1-4*x)*(1-6*x)) +...
%o (PARI) {a(n)=polcoeff(sum(m=0,n,x^m*prod(k=1,m,(1-k*x)/(1-(2*k)*x +x*O(x^n)))),n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 22 2011
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