A124544 Row 4 of rectangular table A124540; equals the self-convolution 4th power of A124534 (row 4 of table A124530).

1, 4, 26, 156, 939, 5764, 36248, 233900, 1549193, 10529052, 73390856, 524300728, 3836318617, 28731858368, 220121136396, 1724083566552, 13798004944813, 112773980097516, 940841899662784, 8008011665402152, 69505777613953576

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..20.

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^4 ]^4, where R_n(x) is the g.f. of row n in table A124540.

Prog

(PARI) {a(n)=local(R); R=vector(n+5, r, vector(n+5, c, 1)); for(i=0, n+4, for(r=0, n+4, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[5])^4+O(x^(n+1)))[n+1]}

Crossrefs

Cf. A124534; A124540 (table); other rows: A124531, A124542, A124543, A124545, A124546.

Sequence in context: A204062 A121767 A092167 * A145840 A302335 A244787

Adjacent sequences: A124541 A124542 A124543 * A124545 A124546 A124547

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved