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%I #18 Jul 30 2014 05:39:41
%S 1,2,3,4,5,2,7,4,3,5,11,6,13,7,3,16,17,6,19,4,7,22,23,8,25,26,9,4,29,
%T 15,31,8,33,17,5,9,37,19,13,10,41,7,43,11,5,46,47,16,49,10,17,52,53,6,
%U 11,56,57,58,59,12,61,62,63,64,13,6,67,34,23,35,71,12,73,37,25,38,7,13
%N Numerators of the triangle T(n,k) = (n*(n+1)/2 + k + 1)/(k+1) for n >= k >= 0.
%C The rational triangle T(n,k) begins:
%C n\k 0 1 2 3 4 5 6 7 8 9 ...
%C 0: 1
%C 1: 2 3/2
%C 2: 4 5/2 2
%C 3: 7 4 3 5/2
%C 4: 11 6 13/3 7/2 3
%C 5: 16 17/2 6 19/4 4 7/2
%C 6: 22 23/2 8 25/4 26/5 9/2 4
%C 7: 29 15 31/3 8 33/5 17/3 5 9/2
%C 8: 37 19 13 10 41/5 7 43/7 11/2 5
%C 9: 46 47/2 16 49/4 10 17/2 52/7 53/8 6 11/2
%C ... reformatted and formula corrected. - _Wolfdieter Lang_, Jul 28 2014
%F a(n,k) = numerator((n*(n+1)/2+k+1)/(k+1)), n >= k >= 0. -_Wolfdieter Lang_, Jul 28 2014
%e The triangle a(n,k) begins:
%e n\k 0 1 2 3 4 5 6 7 8 9 ...
%e 0: 1
%e 1: 2 3
%e 2: 4 5 2
%e 3: 7 4 3 5
%e 4: 11 6 13 7 3
%e 5: 16 17 6 19 4 7
%e 6: 22 23 8 25 26 9 4
%e 7: 29 15 31 8 33 17 5 9
%e 8: 37 19 13 10 41 7 43 11 5
%e 9: 46 47 16 49 10 17 52 53 6 11
%e ... reformatted - _Wolfdieter Lang_, Jul 28 2014
%e First column: A000124. Main diagonal: A145051 from A026741.
%e Alternate main and second diagonal: in A173234.
%t Table[(n*(n+1)/2+k+1)/(k+1) // Numerator, {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 08 2014 *)
%Y Cf. A244840 (denominators).
%K nonn,tabl,easy
%O 0,2
%A _Paul Curtz_, Jul 05 2014
%E Edited: (wrong) name changed. Offset changed to 0 in order to fit with the denominators A244840 and the Mathematica program. Cf. A244840 added. - _Wolfdieter Lang_, Jul 28 2014
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