A124533 Row 3 of rectangular table A124530.

1, 1, 4, 16, 71, 351, 1891, 10888, 66139, 420235, 2775981, 18978873, 133828922, 970678790, 7226115267, 55115404005, 430080085093, 3429311454089, 27912555377062, 231710034354364, 1960247357996533, 16889105788701591

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..21.

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(3n), where R_n(x) is the g.f. of row n in table A124530.

Prog

(PARI) a(n)=local(R); R=vector(n+4, r, vector(n+4, 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[4][n+1]

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124534, A124535, A124536.

Sequence in context: A373959 A231373 A161797 * A227034 A224660 A330610

Adjacent sequences: A124530 A124531 A124532 * A124534 A124535 A124536

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved