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%I #11 Jun 29 2018 04:00:45
%S 1,2,5,17,66,295,1408,7103,37140,199915,1100752,6174851,35179360,
%T 203069441,1185443261,6987897811,41544411702,248853224179,
%U 1500635461876,9103375030686,55521964829070,340282330969943,2094756627157200
%N 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.
%C All monomials in "formal determinant" of Hankel matrix, (i.e., including those with zero coefficient due to cancellation). Upper bound for A019448.
%e 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.
%o (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
%Y Cf. A019448.
%K nonn
%O 1,2
%A _Marc LeBrun_, Jun 26 2001
%E Corrected by _Vladeta Jovovic_, Jul 01 2001
%E Definition corrected by _N. J. A. Sloane_, Mar 12 2009
%E a(13) onward from _Max Alekseyev_, Jan 24 2010
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