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%I #5 Jun 14 2017 00:13:14
%S 1,2,15,156,1995,29658,495922,9140344,183201255,3954149640,
%T 91212812647,2235185965152,57899260705117,1578806923315370,
%U 45158965541429475,1350797823601721136,42141425201135893387,1367978583480857293770
%N Secondary diagonal of rectangular table A124540: a(n) = A124540(n+1,n).
%C In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.
%F a(n) is divisible by (n+1): a(n)/(n+1) = A124549(n).
%o (PARI) a(n)=local(R);R=vector(n+2,r,vector(n+2,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n+1,for(r=0,n+1,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+2)))))); Vec(Ser(R[n+2])^(n+1)+O(x^(n+2)))[n+1]
%Y Cf. A124540, A124549, A124547.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 05 2006