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A124543 Row 3 of rectangular table A124540; equals the self-convolution cube of A124533 (row 3 of table A124530).

%I A124543 #3 Mar 30 2012 18:37:01
%S A124543 1,3,15,73,369,1959,10912,63543,385341,2424988,15788469,106075089,
%T A124543 733801709,5217101283,38060759175,284533309380,2177136417042,
%U A124543 17032924895739,136129119703837,1110507731328900,9240322072954209
%N A124543 Row 3 of rectangular table A124540; equals the self-convolution cube of A124533 (row 3 of table A124530).
%C A124543 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 A124543 G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^3 ]^3, where R_n(x) is the g.f. of row n in table A124540.
%o A124543 (PARI) {a(n)=local(R);R=vector(n+4,r,vector(n+4,c,1)); for(i=0,n+3,for(r=0,n+3,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[4])^3+O(x^(n+1)))[n+1]}
%Y A124543 Cf. A124533; A124540 (table); other rows: A124531, A124542, A124544, A124545, A124546.
%K A124543 nonn
%O A124543 0,2
%A A124543 _Paul D. Hanna_, Nov 05 2006