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A124545 Row 5 of rectangular table A124540; equals the self-convolution 5th power of A124535 (row 5 of table A124530).

%I A124545 #5 Mar 13 2015 22:41:31
%S A124545 1,5,40,285,1995,13976,98665,704810,5107950,37619020,281850156,
%T A124545 2149737335,16700012890,132177206400,1066116496055,8764513792396,
%U A124545 73445461419380,627378087294215,5462723243482985,48480560040789335
%N A124545 Row 5 of rectangular table A124540; equals the self-convolution 5th power of A124535 (row 5 of table A124530).
%C A124545 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 A124545 G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^5 ]^5, where R_n(x) is the g.f. of row n in table A124540.
%o A124545 (PARI) {a(n)=local(R);R=vector(n+6,r,vector(n+6,c,1)); for(i=0,n+5,for(r=0,n+5,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[6])^5+O(x^(n+1)))[n+1]}
%Y A124545 Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124546.
%K A124545 nonn
%O A124545 0,2
%A A124545 _Paul D. Hanna_, Nov 05 2006