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A287704 Triangle read by rows, denominators of T(n,k) = (-1)^(n+k)*binomial(n-1,k)* Bernoulli(n+k)/ (n+k) for n>=1, 0<=k<=n-1.

%I A287704 #16 Jul 28 2017 09:56:18
%S A287704 2,12,1,1,60,1,120,1,84,1,1,63,1,60,1,252,1,24,1,132,1,1,40,1,33,1,
%T A287704 5460,1,240,1,44,1,936,1,12,1,1,33,1,585,1,3,1,1020,1,132,1,910,1,2,1,
%U A287704 680,1,1596,1,1,3276,1,1,1,680,1,1197,1,660,1
%N A287704 Triangle read by rows, denominators of T(n,k) = (-1)^(n+k)*binomial(n-1,k)* Bernoulli(n+k)/ (n+k) for n>=1, 0<=k<=n-1.
%e A287704 1:   2
%e A287704 2:  12,  1
%e A287704 3:   1, 60, 1
%e A287704 4: 120,  1, 84,   1
%e A287704 5:   1, 63,  1,  60,   1
%e A287704 6: 252,  1, 24,   1, 132,    1
%e A287704 7:   1, 40,  1,  33,   1, 5460,  1
%e A287704 8: 240,  1, 44,   1, 936,    1, 12,    1
%e A287704 9:   1, 33,  1, 585,   1,    3,  1, 1020, 1
%p A287704 T := (n, k) -> denom((-1)^(n+k)*binomial(n-1, k)*bernoulli(n+k)/(n+k)):
%p A287704 for n from 1 to 9 do seq(T(n, k), k=0..n-1) od;
%t A287704 T[n_, k_]:=Denominator[(-1)^n*Binomial[n - 1, k] BernoulliB[k + n]/(k + n)]; Table[T[n, k], {n, 11}, {k, 0, n - 1}]//Flatten (* _Indranil Ghosh_, Jul 27 2017 *)
%o A287704 (PARI) T(n, k) = denominator((-1)^n*binomial(n-1,k)*bernfrac(k+n)/(k+n));
%o A287704 tabl(nn) = for (n=1, nn, for (k=0, n-1, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Jul 28 2017
%Y A287704 Numerators in A287703.
%K A287704 nonn,tabl,frac
%O A287704 1,1
%A A287704 _Peter Luschny_, Jun 21 2017