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%I #9 Jun 20 2022 05:33:29
%S 1,1,1,2,5,14,43,140,478,1695,6205,23356,90135,355960,1436755,5922799,
%T 24929035,107136291,470281976,2109608447,9677546281,45434467501,
%U 218478232454,1076855324959,5443845581547,28239060235110,150346623540441,821555490484095
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n+1)/2) / Product_{k=1..n} (1 + x*A(x)^k).
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 +...
%e where
%e A(x) = 1 + x*A(x)/(1+x*A(x)) + x^2*A(x)^3/((1+x*A(x))*(1+x*A(x)^2)) + x^3*A(x)^6/((1+x*A(x))*(1+x*A(x)^2)*(1+x*A(x)^3)) + x^4*A(x)^10/((1+x*A(x))*(1+x*A(x)^2)*(1+x*A(x)^3)*(1+x*A(x)^4)) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0, n, x^m*A^(m*(m+1)/2)/prod(k=1,m,1+x*subst(A,x,x+x*O(x^n))^k)));polcoeff(A, n)}; \\ corrected by _Georg Fischer_, Jun 20 2022
%Y Cf. A221547, A221585.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jan 20 2013
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