A124544 Row 4 of rectangular table A124540; equals the self-convolution 4th power of A124534 (row 4 of table A124530).

1, 4, 26, 156, 939, 5764, 36248, 233900, 1549193, 10529052, 73390856, 524300728, 3836318617, 28731858368, 220121136396, 1724083566552, 13798004944813, 112773980097516, 940841899662784, 8008011665402152, 69505777613953576

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. A124534; A124540 (table); other rows: A124531, A124542, A124543, A124545, A124546.

Programs

PARI

{a(n)=local(R);R=vector(n+5,r,vector(n+5,c,1)); for(i=0,n+4,for(r=0,n+4,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[5])^4+O(x^(n+1)))[n+1]}

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^4 ]^4, where R_n(x) is the g.f. of row n in table A124540.