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A120900 G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108). 3

%I

%S 1,1,2,6,19,62,209,722,2539,9054,32654,118876,436171,1611067,5984943,

%T 22344455,83786875,315397144,1191324649,4513742858,17149228138,

%U 65318912291,249356597492,953902701488,3656057618727,14037222220896

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

%C Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2).

%e A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +...

%e = C(x) * A(x^3*C(x)^4) where

%e C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...

%e is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.

%o (PARI) {a(n)=local(A=1+x,C=(1/x*serreverse(x/(1+2*x+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. A120898, A120899, A000108.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 14 2006

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Last modified October 27 06:19 EDT 2021. Contains 348271 sequences. (Running on oeis4.)