A126461 Column 0 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 3*k - 4)*k/6, k>=0}.

1, 1, 1, 3, 21, 274, 5806, 182766, 8034916, 471517614, 35682799508, 3388864405941, 395127873991296, 55543575452873070, 9271180003481197642, 1813921568747948684475, 411378931233397975750296

Offset: 0

Author

Paul D. Hanna, Dec 27 2006

Keywords

• nonn

Comments

When shifted left, equals column 1 of triangle A126460, which is the number of subpartitions of partition: {(k^2 + 6*k + 5)*k/6, k>=0}.

Examples

			Equals the number of subpartitions of the partition:
{(k^2 + 3*k - 4)*k/6, k>=0} = [0,0,2,7,16,30,50,77,112,156,210,275,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^0 + 1*x^2*(1-x)^2 + 3*x^3*(1-x)^7 + 21*x^4*(1-x)^16 + 274*x^5*(1-x)^30 + 5806*x^6*(1-x)^50 + 182766*x^7*(1-x)^77 ...
		

Crossrefs

Cf. A126460; A126462, 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+3*k-4)*k/6)), n)}

Formula

G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 3*k - 4)*k/6].