A120899 G.f. satisfies: A(x) = C(x)^2 * A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).
1, 2, 5, 16, 54, 186, 654, 2338, 8463, 30938, 114022, 423096, 1579049, 5922512, 22309350, 84354388, 320020227, 1217689680, 4645693038, 17766596202, 68092473570, 261486788434, 1005962436536, 3876412305114, 14960183283203
Offset: 0
Keywords
Examples
A(x) = 1 + 2*x + 5*x^2 + 16*x^3 + 54*x^4 + 186*x^5 + 654*x^6 +... = C(x)^2 * A(x^3*C(x)^4) where C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +... is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.
Crossrefs
Programs
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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^2*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}
Comments