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%I #27 Jul 28 2014 16:27:14
%S 1,1,2,1,2,1,1,1,1,2,1,1,3,2,1,1,2,1,4,1,2,1,2,1,4,5,2,1,1,1,3,1,5,3,
%T 1,2,1,1,1,1,5,1,7,2,1,1,2,1,4,1,2,7,8,1,2,1,2,3,4,1,6,7,8,9,2,1,1,1,
%U 1,2,5,1,7,4,3,5,1,2
%N Denominators of the triangle T(n,k) = (n*(n+1)/2+k+1)/(k+1) for n >= k >= 0.
%C Numerators: A244734(n,k).
%C See A244734 for the first entries of the rational triangle T(n,k).
%F a(n,k) = denominator((n*(n+1)/2 + k + 1)/(k+1)) for n >= k >= 0.
%e T(0,0) = 1/1, T(1,0) = 2/1, T(1,1) = 3/2,... .
%e The triangle a(n,k) begins:
%e n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
%e 0: 1
%e 1: 1 2
%e 2: 1 2 1
%e 3: 1 1 1 2
%e 4: 1 1 3 2 1
%e 5: 1 2 1 4 1 2
%e 6: 1 2 1 4 5 2 1
%e 7: 1 1 3 1 5 3 1 2
%e 8: 1 1 1 1 5 1 7 2 1
%e 9: 1 2 1 4 1 2 7 8 1 2
%e 10: 1 2 3 4 1 6 7 8 9 2 1
%e 11: 1 1 1 2 5 1 7 4 3 5 1 2
%e 12: 1 1 1 2 5 1 7 4 3 5 11 2 1
%e 13: 1 2 3 4 5 6 1 8 9 10 11 12 1 2
%e 14: 1 2 1 4 1 2 1 8 3 2 11 4 13 2 1
%e 15: 1 1 1 1 1 1 7 1 3 1 11 1 13 7 1 2
%e 16: 1 1 3 1 5 3 7 1 9 5 11 3 13 7 15 2 1
%e 17: 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5 16 1 2
%e 18: 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5 16 17 2 1
%e 19: 1 1 3 2 1 3 7 4 9 1 11 6 13 7 3 8 17 9 1 2
%e 20: 1 1 1 2 1 1 1 4 3 1 11 2 13 1 1 8 17 3 19 2 1
%e n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
%e .. reformatted - _Wolfdieter Lang_, Jul 28 2014 .
%e The second column is of period 4: repeat 2, 2, 1, 1. From A014695 or A130658.
%e The third column is of period 3: repeat 1, 1, 3. From A109007.
%e The fourth column is of period 8: repeat 2, 2, 4, 4, 1, 1, 4, 4.
%e The fifth column is of period 5: repeat 1, 1, 5, 5, 5.
%e The sixth column is of period 12: repeat 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3 .
%e The seventh column is of period 7: repeat 1, 1, 7, 7, 7, 7, 7.
%e Hence the positive terms of A022998.
%e Main diagonal: A000034(n).
%e Alternate main and second diagonal: A130658(n).
%e Common denominator by row: 1, 2, 2, 2, 6, 4, 20, 30, 70, ... .
%t Table[(n*(n+1)/2+k+1)/(k+1) // Denominator, {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 08 2014 *)
%Y Cf. A014695, A130658, A109007, A002260, A022998, A244734, A000034.
%K nonn,frac,tabl,easy
%O 0,3
%A _Paul Curtz_, Jul 07 2014
%E Editse: Name reformulated, comment with T(n,k) reference added. - _Wolfdieter Lang_, Jul 28 2014
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