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A331317
Number of nonnegative integer matrices with 2 distinct columns and any number of distinct nonzero rows with each column sum being n and rows in decreasing lexicographic order.
2
0, 1, 4, 15, 44, 120, 319, 804, 1960, 4652, 10782, 24435, 54329, 118663, 254969, 539825, 1127247, 2323811, 4733634, 9535025, 19005218, 37507726, 73333405, 142112298, 273092198, 520612163, 984943887, 1849920530, 3450475858, 6393203485, 11770416017, 21538245911, 39181212114
OFFSET
0,3
COMMENTS
The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.
LINKS
FORMULA
a(n) = A219554(n) - A000009(n).
PROG
(PARI) a(n)={my(p=prod(i=0, n, prod(j=0, n, 1 + x^i*y^j + O(x*x^n) + O(y*y^n))), q=prod(i=1, n, 1 + x^i + O(x*x^n))); polcoef(polcoef(p, n), n)/2 - polcoef(q, n)}
CROSSREFS
Column k=2 of A331160.
Sequence in context: A240359 A282522 A329523 * A259664 A321880 A075673
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 13 2020
STATUS
approved