

A062881


Number of partitions of n^2 into exactly n nonzero parts, such that there are at most one 1's, two 2's... n1 n1's, n n's, n1 n+1's... two 2n2's and one 2n1.


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 3part 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*n1, sum(j=0, nabs(in), (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



