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Triangle read by rows: a(n, k) is the denominator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.
8

%I #17 Oct 21 2019 02:12:18

%S 1,1,1,1,3,1,1,3,2,1,1,1,1,5,1,1,3,2,5,3,1,1,3,1,5,3,7,1,1,1,2,5,1,7,

%T 4,1,1,3,1,1,3,7,2,9,1,1,3,2,5,3,7,4,9,5,1,1,1,1,5,1,7,1,3,5,11,1,1,3,

%U 2,5,3,7,4,9,5,11,6,1,1,3,1,5,3,1,2,9,5,11,3,13,1,1,1,2,1,1,7,4,3,1,11,2

%N Triangle read by rows: a(n, k) is the denominator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.

%C A093412 gives the corresponding numerators.

%C A109613(n+1) - 2 = 2*floor((n+1)/2) - 1 is the largest number in row n. [Corrected by _Petros Hadjicostas_, Oct 20 2019]

%F a(n, k) = (k+1)/gcd(2n+2, k+1).

%e Triangle a(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:

%e 1;

%e 1, 1;

%e 1, 3, 1;

%e 1, 3, 2, 1;

%e 1, 1, 1, 5, 1;

%e 1, 3, 2, 5, 3, 1;

%e 1, 3, 1, 5, 3, 7, 1;

%e 1, 1, 2, 5, 1, 7, 4, 1;

%e 1, 3, 1, 1, 3, 7, 2, 9, 1;

%e ... - _Petros Hadjicostas_, Oct 20 2019

%Y Cf. A109613, A093412, A093413, A093414, A093417.

%K easy,nonn,tabl,frac

%O 1,5

%A _Amarnath Murthy_, Mar 30 2004

%E Edited and extended by _David Wasserman_, Feb 01 2006