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A120916 G.f. satisfies: A(x) = C(2x)*A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108). 3

%I

%S 1,2,8,42,244,1504,9656,63856,431872,2972778,20756036,146627648,

%T 1046060836,7525452296,54530660832,397628393728,2915496099136,

%U 21481907631872,158975372309176,1181109256858096,8806197969093184

%N G.f. satisfies: A(x) = C(2x)*A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).

%C Self-convolution equals A120915, which equals column 0 of triangle A120914 (cascadence of (1+2x)^2).

%o (PARI) {a(n)=local(A=1+2*x,C=(1/x*serreverse(x/(1+4*x+4*x^2+x*O(x^n))))^(1/2)); for(i=0,n,A=C*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}

%Y Cf. A120914, A120915, A000108.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 17 2006

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Last modified September 27 21:12 EDT 2021. Contains 347698 sequences. (Running on oeis4.)