A124546 Row 6 of rectangular table A124540; equals the self-convolution 6th power of A124536 (row 6 of table A124530).

1, 6, 57, 470, 3756, 29658, 233241, 1836912, 14543877, 116087596, 936035298, 7636193394, 63106764294, 528842660346, 4497737044197, 38849799300246, 341016182672523, 3043519729680600, 27629723055323671, 255224042883932790

Offset

0,2

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.

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^6 ]^6, where R_n(x) is the g.f. of row n in table A124540.

Prog

(PARI) {a(n)=local(R); R=vector(n+7, r, vector(n+7, c, 1)); for(i=0, n+6, for(r=0, n+6, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[7])^6+O(x^(n+1)))[n+1]}

Crossrefs

Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124545.

Sequence in context: A261740 A296027 A229280 * A144070 A095900 A161434

Adjacent sequences: A124543 A124544 A124545 * A124547 A124548 A124549

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved