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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. 0
1, 2, 5, 17, 66, 295, 1408, 7103, 37140, 199915, 1100752, 6174851, 35179360, 203069441, 1185443261, 6987897811, 41544411702, 248853224179, 1500635461876, 9103375030686, 55521964829070, 340282330969943, 2094756627157200 (list; graph; refs; listen; history; text; internal format)
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) } [From Max Alekseyev, Jan 24 2010]

CROSSREFS

Cf. A019448.

Sequence in context: A008932 A167809 A262449 * 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

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Last modified February 24 22:41 EST 2018. Contains 299627 sequences. (Running on oeis4.)