A124531 Row 1 of rectangular table A124530.

1, 1, 2, 5, 16, 62, 274, 1332, 6978, 38873, 228090, 1399625, 8933506, 59066261, 403241292, 2835267821, 20490128048, 151951503074, 1154770194362, 8983396031267, 71473650532630, 581142591346325, 4825842125683150

Offset

0,3

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.

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

(PARI) a(n)=local(R); R=vector(n+2, r, vector(n+2, 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[2][n+1]

Crossrefs

Cf. A124530 (table); other rows: A124532, A124533, A124534, A124535, A124536.

Sequence in context: A368318 A369400 A033543 * A129578 A005387 A173469

Adjacent sequences: A124528 A124529 A124530 * A124532 A124533 A124534

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved