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A124532 Row 2 of rectangular table A124530. 7

%I #5 Jun 14 2017 00:11:42

%S 1,1,3,10,39,174,858,4564,25793,153301,951325,6130757,40861658,

%T 280767621,1983859580,14385651988,106878699675,812480791324,

%U 6312686006725,50083418434737,405430892640225,3346568909331984

%N Row 2 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)^(2n), where R_n(x) is the g.f. of row n in table A124530.

%o (PARI) a(n)=local(R);R=vector(n+3,r,vector(n+3,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[3][n+1]

%Y Cf. A124530 (table); other rows: A124531, A124533, A124534, A124535, A124536.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 05 2006

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