A124546 Row 6 of rectangular table A124540; equals the self-convolution 6th power of A124536 (row 6 of table A124530).

1, 6, 57, 470, 3756, 29658, 233241, 1836912, 14543877, 116087596, 936035298, 7636193394, 63106764294, 528842660346, 4497737044197, 38849799300246, 341016182672523, 3043519729680600, 27629723055323671, 255224042883932790

Offset: 0

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124545.

Programs

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]}

Formula

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.