A124543 Row 3 of rectangular table A124540; equals the self-convolution cube of A124533 (row 3 of table A124530).

1, 3, 15, 73, 369, 1959, 10912, 63543, 385341, 2424988, 15788469, 106075089, 733801709, 5217101283, 38060759175, 284533309380, 2177136417042, 17032924895739, 136129119703837, 1110507731328900, 9240322072954209

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)^3 ]^3, where R_n(x) is the g.f. of row n in table A124540.

Prog

(PARI) {a(n)=local(R); R=vector(n+4, r, vector(n+4, c, 1)); for(i=0, n+3, for(r=0, n+3, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[4])^3+O(x^(n+1)))[n+1]}

Crossrefs

Cf. A124533; A124540 (table); other rows: A124531, A124542, A124544, A124545, A124546.

Sequence in context: A232289 A370480 A055837 * A007142 A357222 A224397

Adjacent sequences: A124540 A124541 A124542 * A124544 A124545 A124546

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved