%I #15 Apr 20 2021 17:06:00
%S 1,1,2,5,1,21,2,1,106,11,2,1,643,62,12,2,1,4547,406,71,13,2,1,36696,
%T 3046,481,80,14,2,1,332769,25737,3708,559,89,15,2,1,3349507,242094,
%U 32028,4414,640,98,16,2,1,37054436,2510733,306723,38893,5164,724,107,17,2,1
%N Triangle of numbers a(n,k) = number of permutations on n letters containing k 3-sequences (n >= 0, 0<=k<=max(0,n-2)).
%H J. Riordan, <a href="http://projecteuclid.org/euclid.bams/1183507357">Permutations without 3-sequences</a>, Bull. Amer. Math. Soc., 51 (1945), 745-748.
%F Riordan gives a recurrence.
%e Triangle begins:
%e 1;
%e 1;
%e 2;
%e 5, 1;
%e 21, 2, 1;
%e 106, 11, 2, 1;
%e 643, 62, 12, 2, 1;
%e 4547, 406, 71, 13, 2, 1;
%e 36696, 3046, 481, 80, 14, 2, 1;
%e 332769, 25737, 3708, 559, 89, 15, 2, 1;
%e ...
%Y Columns give A002628, A002629, A002630.
%Y Row sums give A000142.
%K nonn,tabf,nice,easy
%O 0,3
%A _N. J. A. Sloane_
%E Edited and extended by _Max Alekseyev_, Sep 05 2010
%E a(0,0) = a(1,0) = 1 prepended by _Alois P. Heinz_, Apr 20 2021