A062881 Number of partitions of n^2 into exactly n nonzero parts, such that there are at most one 1's, two 2's, ... n-1 n-1's, n n's, n-1 n+1's, ... two 2n-2's and one 2n-1.

1, 2, 5, 17, 66, 295, 1408, 7103, 37140, 199915, 1100752, 6174851, 35179360, 203069441, 1185443261, 6987897811, 41544411702, 248853224179, 1500635461876, 9103375030686, 55521964829070, 340282330969943, 2094756627157200

Offset: 1

Author

Marc LeBrun, Jun 26 2001

Keywords

• nonn

Comments

All monomials in "formal determinant" of Hankel matrix, (i.e., including those with zero coefficient due to cancellation). Upper bound for A019448.

Examples

			a(3) = 5 since the 3-part partitions of 9 meeting the budget for parts (i.e., at most 1 1's, 2 2s, 3 3s, 2 4s and 1 5s) are 1+3+5, 1+4+4, 2+2+5, 2+3+4 and 3+3+3.
		

Crossrefs

Cf. A019448.

Programs

PARI

{ a(n) = polcoeff( polcoeff( prod(i=1,2*n-1, sum(j=0, n-abs(i-n), (x^i*y)^j ) + O(x^(n^2+1)) + O(y^(n+1)) ), n^2, x ), n, y) } \\ Max Alekseyev, Jan 24 2010

Extensions

Corrected by Vladeta Jovovic, Jul 01 2001

Definition corrected by N. J. A. Sloane, Mar 12 2009

a(13) onward from Max Alekseyev, Jan 24 2010