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%I #5 Jun 14 2017 00:11:38
%S 1,1,4,16,71,351,1891,10888,66139,420235,2775981,18978873,133828922,
%T 970678790,7226115267,55115404005,430080085093,3429311454089,
%U 27912555377062,231710034354364,1960247357996533,16889105788701591
%N Row 3 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.
%F G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(3n), where R_n(x) is the g.f. of row n in table A124530.
%o (PARI) a(n)=local(R);R=vector(n+4,r,vector(n+4,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)))))); R[4][n+1]
%Y Cf. A124530 (table); other rows: A124531, A124532, A124534, A124535, A124536.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 05 2006