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%I #7 Mar 30 2012 18:37:26
%S 1,0,0,8,0,0,128,0,0,2560,0,0,60416,0,0,1728512,0,0,63438848,0,0,
%T 3096477696,0,0,196811685888,0,0,15408280109056,0,0,1413600665141248,
%U 0,0,147160243434946560,0,0,17047411713181220864,0,0,2169625122325921792000
%N G.f. C(C(x)) where C(x) is the g.f. of A191417.
%C Functions C(x) and S(x) satisfy: C(C(x)) - S(S(x)) = x and C(x) = x + 2*x^2*S(x), where C(x) is the g.f. of A191417 and S(x) is the g.f. of A191418.
%e G.f. C(C(x)) = x + 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...
%e Related expansions.
%e C(x) = x + 4*x^4 + 32*x^7 + 384*x^10 + 6912*x^13 + 202752*x^16 +...
%e S(x) = 2*x^2 + 16*x^5 + 192*x^8 + 3456*x^11 + 101376*x^14 +...
%e S(S(x)) = 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...
%o (PARI) {a(n)=local(C=x,S=2*x^2,Sv=[0,2]);
%o for(i=0,n\3,Sv=concat(Sv,[0,0,0]);S=x*Ser(Sv);C=x+2*x^2*S;
%o Sv[#Sv]=polcoeff((subst(C,x,C)-subst(S,x,S))/4,#Sv+2););polcoeff(subst(C,x,C),n)}
%Y Cf. A191417 (C(x)), A191418 (S(x)).
%K nonn
%O 1,4
%A _Paul D. Hanna_, Jun 01 2011
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