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A331316
Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with each column sum being 2 and rows in decreasing lexicographic order.
3
1, 1, 4, 27, 266, 3599, 62941, 1372117, 36248765, 1135864306, 41501271477, 1743624004536, 83268125043937, 4476101995389591, 268589319338401864, 17860954789864760357, 1307982591075162739660, 104895999816356419875935, 9166919404389461922512723
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) = Sum_{k=0..n} Stirling1(n,k)*A094574(k).
EXAMPLE
The a(2) = 4 matrices are:
[2 1] [2 0] [1 2] [1 1]
[0 1] [0 2] [1 0] [1 0]
[0 1]
CROSSREFS
Row n=2 of A331160.
Cf. A094574.
Sequence in context: A218653 A359461 A121353 * A353233 A265270 A161633
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 13 2020
STATUS
approved