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%I #8 Dec 05 2016 02:41:24
%S 1,2,3,3,11,12,4,32,132,60,5,84,1152,2664,360,6,208,9072,93312,80640,
%T 2520,7,496,67392,2944512,14169600,3412800,20160,8,1152,482112,
%U 87588864,2239488000,3608064000,192326400,181440,9,2624,3359232,2508226560
%N Table read by antidiagonals: T(n,k) = count of increasing runs in strings of length n*k formed by concatenating k permutations of [n].
%C The first column T(n,1) is A001710(n+1), i.e., (n+1)!/2. The 2nd column T(n,2) is the outer diagonal of triangle A122823.
%F T(n,k) = (k(n+1)/2 - (k-1)(n-1)/2n) * (n!)^k.
%e Table begins:
%e 1 2 3 4 ...
%e 3 11 32 84 ...
%e 12 132 1152 9072 ...
%e 60 2664 93312 2944512 ...
%e ...
%e Example: Take the permutations of [2], namely, 12 and 21, and form all possible strings that are concatenations of 2 of these permutations. These are 1212, 1221, 2112, 2121 with 2, 3, 3, 3 increasing runs respectively. T(2,2) = 2 + 3 + 3 + 3 = 11.
%Y Cf. A001710, A110952, A122823.
%K easy,nonn,tabl
%O 1,2
%A _David Scambler_, Nov 22 2006
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