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G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+5,6).
3

%I #4 Mar 30 2012 18:37:26

%S 1,1,2,10,74,782,10982,206346,5142544,168789842,7201158787,

%T 391194813232,26651992683511,2239377066821882,229147222941318059,

%U 28241058833042859637,4149246030879282392144,720738467750916348374860,146838784937226592635807695

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+5,6).

%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 74*x^4 + 782*x^5 + 10982*x^6 +...

%e where the g.f. satisfies:

%e A(x) = 1 + x*A(x) + x^2*A(x)^7 + x^3*A(x)^28 + x^4*A(x)^84 + x^5*A(x)^210 + x^6*A(x)^462 + x^7*A(x)^924 +...+ x^n*A(x)^(n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/6!) +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^binomial(m+5,6)));polcoeff(A,n)}

%Y Cf. A107591, A191809, A191810, A191811.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 16 2011