A322255 - OEIS

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

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..43.

FORMULA

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

EXAMPLE

Irregular triangle starts:

n\k| 1 2 3 4 5

---+---------------------------------

2 | 2;