A124538 Antidiagonal sums of rectangular table A124530.

1, 2, 3, 5, 11, 33, 125, 551, 2695, 14258, 80343, 477161, 2964299, 19155014, 128203704, 885830074, 6302476880, 46077527307, 345590801495, 2655466079629, 20880388012659, 167861200630015, 1378589193074514, 11558511053625488

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).

Programs

PARI

a(n)=local(R);R=vector(n+1,r,vector(n+1,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)))))); sum(k=0,n,R[n-k+1][k+1])