login
Row 4 of rectangular table A124530.
7

%I #5 Jun 14 2017 00:11:40

%S 1,1,5,25,113,608,3535,21844,141809,959882,6738850,48877221,365145267,

%T 2803002587,22066904802,177881536038,1466278969213,12345543329079,

%U 106069531868783,929158597546721,8292429187449462,75348425058995464

%N Row 4 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)^(4n), where R_n(x) is the g.f. of row n in table A124530.

%o (PARI) a(n)=local(R);R=vector(n+5,r,vector(n+5,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[5][n+1]

%Y Cf. A124530 (table); other rows: A124531, A124532, A124533, A124535, A124536.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 05 2006