A126463 Column 3 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.

1, 1, 10, 195, 5940, 257300, 14989472, 1130000385, 107089958760, 12470885416545, 1751753684302150, 292264756622072214, 57165584968923450000, 12962148519535236156640, 3374220800446022166695530

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 12*k + 41)*k/6].

Example

Equals the number of subpartitions of the partition:
{(k^2 + 12*k + 41)*k/6, k>=0} = [0,9,23,43,70,105,149,203,268,345,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^9 + 10*x^2*(1-x)^23 + 195*x^3*(1-x)^43 + 5940*x^4*(1-x)^70 + 257300*x^5*(1-x)^105 + 14989472*x^6*(1-x)^149 + 1130000385*x^7*(1-x)^203 ...

Prog

(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+12*k+41)*k/6)), n)}

Crossrefs

Cf. A126460; A126461, A126462, A126464.

Sequence in context: A361311 A007816 A365176 * A239766 A294047 A239768

Adjacent sequences: A126460 A126461 A126462 * A126464 A126465 A126466

Keyword

nonn

Author

Paul D. Hanna, Dec 27 2006

Status

approved