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%I #3 Mar 30 2012 18:37:01
%S 1,2,8,44,302,2437,22143,220663,2377322,27462836,338270681,4422338285,
%T 61114545578,889542935517,13593252066134,217461100417945,
%U 3632859088845390,63233532604594586,1144455373221119025
%N Main diagonal of rectangular table A124460.
%C In table A124460, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.
%o (PARI) {a(n)=local(R=vector(n+1,r,vector(n+1,c,binomial(r+c-2,c-1)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^r+O(x^(n+1))))));R[n+1][n+1]}
%Y Cf. A124460 (table); rows: A124461, A124462, A124463, A124464, A124465, A124466; A124468 (diagonal).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 03 2006
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