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%I #3 Mar 30 2012 18:37:04
%S 1,1,2,4,9,24,77,295,1329,6924,41030,272271,1996406,16000511,
%T 138953665,1298206570,12969761907,137846434950,1551712558368,
%U 18429620298121,230175973108212,3014142623764514,41275488455847862,589698136493691293
%N G.f.: A(x) = 1 + Sum_{n>=1} x^n*[ Product_{k=1..n} F_k(x) ] where F_n(x) = 1 + x*F_n(x)^n.
%e A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 24*x^5 + 77*x^6 + 295*x^7 +...
%e A(x) = 1 + x*F_1(x) + x^2*F_1(x)*F_2(x) + x^3*F_1(x)*F_2(x)*F_3(x) +...
%e where F_n(x) = Sum_{k>=0} C(n*k,k)/((n-1)*k + 1)*x^k:
%e F_1(x) = 1/(1-x);
%e F_2(x) = 1 + x + 2x^2 + 5x^3 + 14x^4 + 42x^5 + +... (A000108);
%e F_3(x) = 1 + x + 3x^2 + 12x^3 + 55x^4 + 273x^5 + ...(A001764);
%e F_4(x) = 1 + x + 4x^2 + 22x^3 + 140x^4 + 969x^5 +...(A002293); ...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(k=0,n,A=1+x*A* Ser(vector(n+1,i,binomial((n-k+1)*(i-1),i-1)/((n-k)*(i-1)+1)))); polcoeff(A,n) }
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 03 2007
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