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%I #5 Mar 13 2015 00:43:51
%S 1,6,57,470,3756,29658,233241,1836912,14543877,116087596,936035298,
%T 7636193394,63106764294,528842660346,4497737044197,38849799300246,
%U 341016182672523,3043519729680600,27629723055323671,255224042883932790
%N Row 6 of rectangular table A124540; equals the self-convolution 6th power of A124536 (row 6 of table A124530).
%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 G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^6 ]^6, where R_n(x) is the g.f. of row n in table A124540.
%o (PARI) {a(n)=local(R);R=vector(n+7,r,vector(n+7,c,1)); for(i=0,n+6,for(r=0,n+6,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[7])^6+O(x^(n+1)))[n+1]}
%Y Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124545.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 05 2006
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