A124467 Main diagonal of rectangular table A124460.

1, 2, 8, 44, 302, 2437, 22143, 220663, 2377322, 27462836, 338270681, 4422338285, 61114545578, 889542935517, 13593252066134, 217461100417945, 3632859088845390, 63233532604594586, 1144455373221119025

Offset: 0

Author

Paul D. Hanna, Nov 03 2006

Keywords

• nonn

Comments

In table A124460, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.

Crossrefs

Cf. A124460 (table); rows: A124461, A124462, A124463, A124464, A124465, A124466; A124468 (diagonal).

Programs

PARI

{a(n)=local(R=vector(n+1,r,vector(n+1,c,binomial(r+c-2,c-1)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^r+O(x^(n+1))))));R[n+1][n+1]}