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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 first occurrence of a smallest part, n>=1, 1<=k<=n.
1

%I #10 Feb 26 2014 08:55:22

%S 1,2,0,3,1,0,6,2,0,0,10,5,1,0,0,20,9,3,0,0,0,37,19,7,1,0,0,0,72,36,16,

%T 4,0,0,0,0,140,71,33,11,1,0,0,0,0,275,139,67,26,5,0,0,0,0,0,540,274,

%U 135,58,16,1,0,0,0,0,0,1069,539,269,123,42,6,0,0,0,0,0,0,2118,1068,534,254,99,22,1,0

%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 first occurrence of a smallest part, n>=1, 1<=k<=n.

%C Column k=0 is A238351. Column k=1 is A171682.

%C Row sums are A011782.

%H Joerg Arndt, <a href="/A238347/b238347.txt">Table of n, a(n) for n = 1..465</a> (rows 1..30, flattened)

%e Triangle starts:

%e 01: 1,

%e 02: 2, 0,

%e 03: 3, 1, 0,

%e 04: 6, 2, 0, 0,

%e 05: 10, 5, 1, 0, 0,

%e 06: 20, 9, 3, 0, 0, 0,

%e 07: 37, 19, 7, 1, 0, 0, 0,

%e 08: 72, 36, 16, 4, 0, 0, 0, 0,

%e 09: 140, 71, 33, 11, 1, 0, 0, 0, 0,

%e 10: 275, 139, 67, 26, 5, 0, 0, 0, 0, 0,

%e 11: 540, 274, 135, 58, 16, 1, 0, 0, 0, 0, 0,

%e 12: 1069, 539, 269, 123, 42, 6, 0, 0, 0, 0, 0, 0,

%e 13: 2118, 1068, 534, 254, 99, 22, 1, 0, 0, 0, 0, 0, 0,

%e 14: 4206, 2117, 1062, 516, 220, 64, 7, 0, 0, 0, 0, 0, 0, 0,

%e 15: 8365, 4205, 2111, 1040, 470, 163, 29, 1, 0, 0, 0, 0, 0, 0, 0,

%e ...

%K nonn,tabl

%O 1,2

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