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

1,2

Comments

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

Links

Table of n, a(n) for n=1..23.

Example

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.

Prog

(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

Crossrefs

Cf. A019448.

Sequence in context: A262449 A346506 A362967 * A122206 A104082 A166474

Adjacent sequences: A062878 A062879 A062880 * A062882 A062883 A062884

Keyword

nonn

Author

Marc LeBrun, Jun 26 2001

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

Status

approved