A382597 a(n) = Product_{i=1..n} 1 - i + n*(n - i + 1) - (n - 2*i + 1)*((n - i + 1) mod 2).

1, 1, 8, 105, 3840, 181545, 15814656, 1635491025, 261144576000, 47396578806225, 12046266925056000, 3390530144534798265, 1256223498048110592000, 506594307608708171477625, 257699484814807738928332800, 140934799049120316306629726625, 94240120920042785192632469422080

Offset: 0

Author

Stefano Spezia, Mar 31 2025

Keywords

• nonn

Comments

a(n) is the product of the elements of the main antidiagonal of the n X n square matrix M(n) formed by writing the numbers 1, ..., n^2 successively forward and backward along the rows in zig-zag pattern (see A317614).

Except for n = 0, 2, and 6, a(n) has trailing zeros iff n is even.

Examples

			a(4) = 3840:
   1,  2,  3,  4;
   8,  7,  6,  5;
   9, 10, 11, 12;
  16, 15, 14, 13.
		

Crossrefs

Cf. A317614, A370753, A382532.

Programs

Mathematica

a[n_]:=Product[1-i+n(n-i+1)-(n-2i+1)Mod[n-i+1,2],{i,n}]; Array[a,17,0]