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A306641 A(n,k) = Sum_{j=0..n} (k*n)!/(j! * (n-j)!)^k, square array A(n,k) read by antidiagonals, for n >= 0, k >= 0. 4
1, 1, 2, 1, 2, 3, 1, 4, 4, 4, 1, 12, 36, 8, 5, 1, 48, 900, 400, 16, 6, 1, 240, 45360, 94080, 4900, 32, 7, 1, 1440, 3855600, 60614400, 11988900, 63504, 64, 8, 1, 10080, 493970400, 82065984000, 114144030000, 1704214512, 853776, 128, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Columns are the number of maximal chains to multiples of J in the graded poset of (2 X n) antimagic squares. See Stanley. - Arnav Krishna, Jan 13 2023
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Vol I, Exercise 53, p. 540.
LINKS
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
2, 2, 4, 12, 48, ...
3, 4, 36, 900, 45360, ...
4, 8, 400, 94080, 60614400, ...
5, 16, 4900, 11988900, 114144030000, ...
6, 32, 63504, 1704214512, 249344297250048, ...
CROSSREFS
Columns 0-3 give A000027(n+1), A000079, A002894, A306642, A345646.
Rows 0-1 give A000012, A208529(n+2).
Main diagonal gives A306644.
Sequence in context: A110582 A162507 A091298 * A055884 A055889 A125930
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 02 2019
STATUS
approved

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Last modified February 22 09:09 EST 2024. Contains 370250 sequences. (Running on oeis4.)