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%I #10 Mar 30 2012 18:37:31
%S 1,1,2,6,30,170,1242,9534,86118,797778,8327410,88438966,1032534190,
%T 12233231738,156832510922,2038914853870,28368720701302,
%U 400233587440290,5994141844357346,91033137985948774,1458360235236325182,23691777860254217802,403933868741833240506
%N G.f. satisfies: A( x*A(-x)/A(x) ) = 1 + x.
%F G.f. satisfies: A(x) = 1 + x*A(A(x) - 1)/A(1 - A(x)).
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 30*x^4 + 170*x^5 + 1242*x^6 +...
%e Related expansions.
%e x*A(-x)/A(x) = x - 2*x^2 + 2*x^3 - 10*x^4 + 18*x^5 - 290*x^6 + 594*x^7 +...
%e A(A(x)-1) = 1 + x + 4*x^2 + 20*x^3 + 128*x^4 + 928*x^5 + 7636*x^6 +...
%e A(1-A(x)) = 1 - x - 4*x^3 - 4*x^4 - 112*x^5 - 288*x^6 - 6436*x^7 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+serreverse(x*subst(A,x,-x)/(A+x*O(x^n))));polcoeff(A,n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 04 2011
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