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%I #20 May 20 2023 05:17:55
%S 2,6,24,2,120,14,720,90,2,5040,646,32,40320,5242,368,2,362880,47622,
%T 3984,72,3628800,479306,44304,1496,2,39916800,5296790,521606,25384,
%U 160,479001600,63779034,6564318,399848,6056,2,6227020800,831283558,88422296,6231544,161136,352
%N 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).
%F T(n,k) = Sum_{j=k..floor(n/2)} A129534(n,j). - _Alois P. Heinz_, May 20 2023
%e Irregular triangle starts:
%e n\k| 1 2 3 4 5
%e ---+---------------------------------
%e 2 | 2;
%e 3 | 6;
%e 4 | 24, 2;
%e 5 | 120, 14;
%e 6 | 720, 90, 2;
%e 7 | 5040, 646, 32;
%e 8 | 40320, 5242, 368, 2;
%e 9 | 362880, 47622, 3984, 72;
%e 10 | 3628800, 479306, 44304, 1496, 2;
%Y Cf. A000142, A002464, A127697, A129534, A179957-A179967.
%K nonn,tabf
%O 2,1
%A _Seiichi Manyama_, Dec 01 2018
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