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%I #2 Mar 31 2012 20:25:47
%S 2,7,11,15,96,132,26,378,2088,2664,40,1040,12960,66240,80640,57,2325,
%T 51600,594000,2894400,3412800,77,4536,157500,3225600,35380800,
%U 166924800,192326400,100,8036,402192,12877200,251193600,2667168000,12294374400
%N Triangle read by rows: T(n,k) = count of increasing runs in two concatenated k-permutations of [n].
%F T(n,k) = ((k+1) - (n-1)/2n) * Permute(n,k)^2
%e Triangle begins:
%e 2
%e 7 11
%e 15 96 132
%e Take the 2-permutations of [2] namely 12 and 21 and form all possible strings that are concatenations of two 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 Column 1 = T(n, 1) = A005449, Second pentagonal numbers: n*(3n+1)/2.
%K easy,nonn,tabl
%O 1,1
%A _David Scambler_, Oct 29 2006
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