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%I #3 Mar 31 2012 20:25:47
%S 1,3,1,12,5,1,60,28,7,1,360,180,50,9,1,2520,1320,390,78,11,1,20160,
%T 10920,3360,714,112,13,1,181440,100800,31920,7056,1176,152,15,1,
%U 1814400,1028160,332640,75600,13104,1800,198,17,1
%N Triangle read by rows: T[n,k] = the number of ascending runs of length at least k in the permutations of [n] for k <= n.
%C Column T[n,1] is essentially A001710 - all ascending runs in permutations of [n] Column T[n,2] is A006157 - ascending runs of length at least 2 in permutations of [n] Column T[n,3] is A005460 - ascending runs of length at least 3 in permutations of [n]
%F T[n,k] = n![k(n-k+1)+1]/(k+1)! for 0<k<=n; T[n,k] = Sum_{j=k..n}A122843(n,j) (partial row sums of A122843)
%e 1
%e 3 1
%e 12 5 1 ; there are 5 ascending runs of length at least 2 in the permutations of [3], namely 13 in 132 and in 213, 23 in 231, 12 in 312, 123 in 123. T[3,2] = 5.
%Y Cf. A122844, A001710, A006157, A005460.
%K easy,nonn,tabl
%O 1,2
%A _David Scambler_, Sep 13 2006
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