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.

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

Offset: 0

Author

Seiichi Manyama, Mar 02 2019

Keywords

• nonn
• tabl

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

Examples

			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, ...
		

References

• R. P. Stanley, Enumerative Combinatorics, Vol I, Exercise 53, p. 540.

Links

• Seiichi Manyama, Antidiagonals n = 0..49, flattened

Crossrefs

Columns 0-3 give A000027(n+1), A000079, A002894, A306642, A345646.

Rows 0-1 give A000012, A208529(n+2).

Main diagonal gives A306644.