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%I #11 Mar 01 2016 23:38:43
%S 1,1,1,9,9,1,4,1,4,1,5,5,5,5,1,9,9,1,9,9,1,7,7,7,7,7,7,1,8,1,8,1,8,1,
%T 8,1,27,27,1,27,27,1,27,27,1,5,5,5,5,1,5,5,5,5,1
%N Denominators of the rational number triangle R(m, a) = - a*(m - a)*(m - 2*a)/(6*m), m >= 1, a = 1, ..., m.
%C For the numerators see A268917.
%C For details and the Hurwitz reference see A267863.
%F T(m, a) = denominator(R(m, a)) with R(m, a) = - a*(m - a)*(m - 2*a)/(6*m), m >= 1, a = 1, ..., m.
%e The triangle T(m, a) begins:
%e m\a 1 2 3 4 5 6 7 8 9 10 11 12 ...
%e 1: 1
%e 2: 1 1
%e 3: 9 9 1
%e 4: 4 1 4 1
%e 5: 5 5 5 5 1
%e 6: 9 9 1 9 9 1
%e 7: 7 7 7 7 7 7 1
%e 8: 8 1 8 1 8 1 8 1
%e 9: 27 27 1 27 27 1 27 27 1
%e 10: 5 5 5 5 1 5 5 5 5 1
%e 11: 11 11 11 11 11 11 11 11 11 11 1
%e 12: 36 9 4 9 36 1 36 9 4 9 36 1
%e ...
%e For the triangle of the rationals R(m, a) see A268917.
%t Denominator@ Table[-a (m - a) (m - 2 a)/(6 m), {m, 12}, {a, m}] // Flatten (* _Michael De Vlieger_, Feb 26 2016 *)
%o (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(denominator(- k*(n-k)*(n-2*k)/(6*n)), ", ");); print(););} \\ _Michel Marcus_, Feb 26 2016
%Y Cf. A268917.
%K nonn,frac,tabl,easy
%O 1,4
%A _Wolfdieter Lang_, Feb 25 2016
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