cp's OEIS Frontend

A092741 Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding both the 132- and the 321-pattern is equal to k.

%I A092741 #6 Sep 18 2017 13:06:41
%S A092741 1,0,2,0,2,4,0,8,9,7,0,40,45,24,11,0,240,270,144,50,16,0,1680,1890,
%T A092741 1008,350,90,22,0,13440,15120,8064,2800,720,147,29,0,120960,136080,
%U A092741 72576,25200,6480,1323,224,37,0,1209600,1360800,725760,252000,64800,13230
%N A092741 Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding both the 132- and the 321-pattern is equal to k.
%C A092741 Row sums are the factorial numbers (A000142).
%C A092741 T(n,2)=n!/3 for n>=3 (A002301). T(n,3)=3n!/8 for n>=4.
%C A092741 Diagonal yields A000124.
%H A092741 E. Deutsch and W. P. Johnson, <a href="http://www.jstor.org/stable/3219101">Create your own permutation statistics</a>, Math. Mag., 77, 130-134, 2004.
%H A092741 R. Simion and F. W. Schmidt, <a href="https://doi.org/10.1016/S0195-6698(85)80052-4">Restricted permutations</a>, European J. Combin., 6, 383-406, 1985.
%F A092741 T(n, k) = n!k/[2(k-2)!(k+1)] for k<n; T(n, n) = n(n-1)/2.
%e A092741 T(3,2)=2 because only 132 and 321 satisfy the requirements.
%Y A092741 Cf. A000142, A002301, A000124.
%K A092741 nonn,tabl
%O A092741 1,3
%A A092741 _Emeric Deutsch_, Apr 12 2004