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A062881
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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.
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0
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| All monomials in "formal determinant" of Hankel matrix, (i.e. including those with zero coefficient due to cancellation). Upper bound for A019448.
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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.
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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 (maxale(AT)gmail.com), Jan 24 2010]
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CROSSREFS
| Cf. A019448.
Sequence in context: A052539 A008932 A167809 * A122206 A104082 A166474
Adjacent sequences: A062878 A062879 A062880 * A062882 A062883 A062884
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KEYWORD
| nonn
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AUTHOR
| Marc LeBrun (mlb(AT)well.com), Jun 26 2001
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EXTENSIONS
| Corrected by Vladeta Jovovic (vladeta(AT)EUnet.yu) Jul 01, 2001.
Definition corrected by N. J. A. Sloane, Mar 12 2009
a(13) onward from Max Alekseyev (maxale(AT)gmail.com), Jan 24 2010
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