cp's OEIS Frontend

A191812 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+5,6).

%I A191812 #8 Jan 29 2025 15:00:56
%S A191812 1,1,2,10,74,782,10982,206346,5142544,168789842,7201158787,
%T A191812 391194813232,26651992683511,2239377066821882,229147222941318059,
%U A191812 28241058833042859637,4149246030879282392144,720738467750916348374860,146838784937226592635807695
%N A191812 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+5,6).
%e A191812 G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 74*x^4 + 782*x^5 + 10982*x^6 +...
%e A191812 where the g.f. satisfies:
%e A191812 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 A191812 (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 A191812 Cf. A107591, A191809, A191810, A191811.
%K A191812 nonn
%O A191812 0,3
%A A191812 _Paul D. Hanna_, Jun 16 2011