%I #5 Jun 14 2017 00:12:25
%S 1,2,3,5,11,33,125,551,2695,14258,80343,477161,2964299,19155014,
%T 128203704,885830074,6302476880,46077527307,345590801495,
%U 2655466079629,20880388012659,167861200630015,1378589193074514,11558511053625488
%N Antidiagonal sums of rectangular table A124530.
%C In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.
%o (PARI) a(n)=local(R);R=vector(n+1,r,vector(n+1,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); sum(k=0,n,R[n-k+1][k+1])
%Y Cf. A124530 (table).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 05 2006