A322255 Triangle T(n,k) giving the number of permutations of 1..n with no adjacent elements within k in value, for n >= 2, 1 <= k <= floor(n/2).

2, 6, 24, 2, 120, 14, 720, 90, 2, 5040, 646, 32, 40320, 5242, 368, 2, 362880, 47622, 3984, 72, 3628800, 479306, 44304, 1496, 2, 39916800, 5296790, 521606, 25384, 160, 479001600, 63779034, 6564318, 399848, 6056, 2, 6227020800, 831283558, 88422296, 6231544, 161136, 352

Offset: 2

Author

Seiichi Manyama, Dec 01 2018

Keywords

• nonn
• tabf

Examples

			Irregular triangle starts:
n\k|       1       2      3     4  5
---+---------------------------------
2  |       2;
3  |       6;
4  |      24,      2;
5  |     120,     14;
6  |     720,     90,     2;
7  |    5040,    646,    32;
8  |   40320,   5242,   368,    2;
9  |  362880,  47622,  3984,   72;
10 | 3628800, 479306, 44304, 1496, 2;
		

Crossrefs

Cf. A000142, A002464, A127697, A129534, A179957-A179967.

Formula

T(n,k) = Sum_{j=k..floor(n/2)} A129534(n,j). - Alois P. Heinz, May 20 2023