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%I #7 Jun 16 2013 01:02:30
%S 1,2,22,256,3174,40862,539376,7247448,98684230,1357638124,18831752122,
%T 262974273200,3692853486768,52102851020154,738102882420440,
%U 10492839572260176,149623214762194182,2139329701502229300,30661862088900836964,440404155129948147776
%N G.f.: 1 / sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5) where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.
%F Sum_{k=0..n} a(n-k)*a(k) = Sum_{k=0..n} C(3*n+2*k,n-k)*C(3*n-2*k,k).
%F Self-convolution equals A226705.
%e G.f.: A(x) = 1 + 2*x + 22*x^2 + 256*x^3 + 3174*x^4 + 40862*x^5 +...
%e A related series is G(x) = 1 + x*G(x), which begins
%e G(x) = 1 + x + 6*x^2 + 51*x^3 + 506*x^4 + 5481*x^5 + 62832*x^6 +...
%e where A(x) = 1/sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5).
%o (PARI) {a(n)=local(G=1+x); for(i=0, n,G=1+x*G^6+x*O(x^n)); polcoeff(1/sqrt(1+12*x*G^4-16*x*G^5), n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A226705, A183160, A002295.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 15 2013
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