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

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

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.

Crossrefs

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

Programs

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]}

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.