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%I #2 Mar 30 2012 18:37:20
%S 1,0,12,56,5404,171664,193729840,36639136064,919064160383600,
%T 937227332865348224,699214061851483321467008,
%U 3577364560049979516493456896,93123865010226899737836259608990464
%N G.f.: C(x)^2 - S(x)^2 where C(x) = Sum_{n>=0} log(1 - 2^(2n)*x)^(2n)/(2n)! and S(x) = Sum_{n>=0} -log(1 - 2^(2n+1)*x)^(2n+1)/(2n+1)! are the g.f.s of A166995 and A166996, respectively.
%F G.f.: [C(x)+S(x)]*[C(x)-S(x)] where C(x) + S(x) = g.f. of A060690 and C(-x) - S(-x) = g.f. of A014070.
%F Self-convolution of A166998.
%e G.f: 1 + 12*x^2 + 56*x^3 + 5404*x^4 + 171664*x^5 + 193729840*x^6 +...
%e which equals C(x)^2 - S(x)^2 where
%e C(x) = 1 + 8*x^2 + 32*x^3 + 2848*x^4 + 87808*x^5 + 97425920*x^6 +...
%e S(x) = 2*x + 2*x^2 + 88*x^3 + 1028*x^4 + 289184*x^5 + 22451552*x^6 +...
%e Related expansions:
%e C(x) + S(x) = 1 + 2*x + 10*x^2 + 120*x^3 + 3876*x^4 + 376992*x^5 +...
%e C(x) - S(x) = 1 - 2*x + 6*x^2 - 56*x^3 + 1820*x^4 - 201376*x^5 +...
%o (PARI) {a(n)=polcoeff(sum(k=0,n,log(1-2^(2*k)*x +x*O(x^n))^(2*k)/(2*k)!)^2-sum(k=0,n,log(1-2^(2*k+1)*x +x*O(x^n))^(2*k+1)/(2*k+1)!)^2,n)}
%Y Cf. A166995, A166996, A166998, A060690, A014070.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 22 2009
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