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Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n where the k-th part is the last occurrence of a largest part, n>=1, 1<=k<=n.
1

%I #11 Feb 26 2014 11:26:01

%S 1,1,1,2,1,1,3,3,1,1,5,5,4,1,1,8,9,8,5,1,1,14,15,15,12,6,1,1,24,27,27,

%T 24,17,7,1,1,43,47,50,46,37,23,8,1,1,77,85,90,89,75,55,30,9,1,1,140,

%U 153,165,167,152,118,79,38,10,1,1,256,279,301,313,299,250,180,110,47,11,1,1,472,511,552,582,578,516,398,267,149,57,12,1,1

%N Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n where the k-th part is the last occurrence of a largest part, n>=1, 1<=k<=n.

%C Column k=1: T(n,1) = A079500(n-1) = A007059(n).

%C Row sums are A011782.

%H Joerg Arndt, <a href="/A238346/b238346.txt">Table of n, a(n) for n = 1..465</a> (rows 1..30, flattened)

%e Triangle starts:

%e 01: 1,

%e 02: 1, 1,

%e 03: 2, 1, 1,

%e 04: 3, 3, 1, 1,

%e 05: 5, 5, 4, 1, 1,

%e 06: 8, 9, 8, 5, 1, 1,

%e 07: 14, 15, 15, 12, 6, 1, 1,

%e 08: 24, 27, 27, 24, 17, 7, 1, 1,

%e 09: 43, 47, 50, 46, 37, 23, 8, 1, 1,

%e 10: 77, 85, 90, 89, 75, 55, 30, 9, 1, 1,

%e 11: 140, 153, 165, 167, 152, 118, 79, 38, 10, 1, 1,

%e 12: 256, 279, 301, 313, 299, 250, 180, 110, 47, 11, 1, 1,

%e 13: 472, 511, 552, 582, 578, 516, 398, 267, 149, 57, 12, 1, 1,

%e ...

%K nonn,tabl

%O 1,4

%A _Joerg Arndt_ and _Alois P. Heinz_, Feb 25 2014