A124536 Row 6 of rectangular table A124530.

1, 1, 7, 49, 343, 2401, 9430, 65810, 480077, 3637345, 28502254, 230271472, 1913354190, 16318251874, 142611810220, 1275372111383, 11657396456231, 108792892306605, 1035708759921763, 10049835806235885, 99321845447658052

Offset: 0

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124533, A124534, A124535.

Programs

PARI

a(n)=local(R);R=vector(n+7,r,vector(n+7,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[7][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(6n), where R_n(x) is the g.f. of row n in table A124530.