%I #8 Mar 30 2012 18:37:32
%S 1,2,9,59,462,4011,37253,362877,3662590,38001809,403118473,4354812135,
%T 47769686769,530912871966,5968147436150,67766781921248,
%U 776407323511627,8967754230210974,104351087348892229,1222602680134075216,14416253295843685409,171018068867340738997
%N G.f.: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n+1)/2) * (1 - A(x)^(n+1))/(1 - A(x)).
%e G.f.: A(x) = 1 + 2*x + 9*x^2 + 59*x^3 + 462*x^4 + 4011*x^5 + 37253*x^6 +...
%e where the g.f. A = A(x) satisfies the equivalent expressions:
%e A = 1 + x*A*(1-A^2)/(1-A) + x^2*A^3*(1-A^3)/(1-A) + x^3*A^6*(1-A^4)/(1-A) + x^4*A^10*(1-A^5)/(1-A) + x^5*A^15*(1-A^6)/(1-A) +...
%e A = 1 + x*(A + A^2) + x^2*(A^3 + A^4 + A^5) + x^3*(A^6 + A^7 + A^8 + A^9) + x^4*(A^10 + A^11 + A^12 + A^13 + A^14) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,x^m*A^(m*(m+1)/2)*sum(k=0,m,A^k)+x*O(x^n)));polcoeff(A,n)}
%Y Cf. A199544, A199410.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 07 2011