A126462 Column 2 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.

1, 1, 6, 75, 1565, 48950, 2145626, 125727238, 9507150815, 902519025315, 105203477607220, 14786330708536422, 2467862211341410635, 482812610434512386665, 109492763990117261581870

Offset: 0

Author

Paul D. Hanna, Dec 27 2006

Keywords

• nonn

Examples

			Equals the number of subpartitions of the partition:
{(k^2 + 9*k + 20)*k/6, k>=0} = [0,5,14,28,48,75,110,154,208,273,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^5 + 6*x^2*(1-x)^14 + 75*x^3*(1-x)^28 + 1565*x^4*(1-x)^48 + 48950*x^5*(1-x)^75 + 2145626*x^6*(1-x)^110 + 125727238*x^7*(1-x)^154 ...
		

Crossrefs

Cf. A126460; A126461, A126463, A126464.

Programs

PARI

{a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+9*k+20)*k/6)), n)}

Formula

G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 9*k + 20)*k/6].