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.

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, 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, 680, 1, 1596, 1, 1, 3276, 1, 1, 1, 680, 1, 1197, 1, 660, 1

Offset: 1

Author

Peter Luschny, Jun 21 2017

Keywords

• nonn
• tabl
• frac

Examples

			1:   2
2:  12,  1
3:   1, 60, 1
4: 120,  1, 84,   1
5:   1, 63,  1,  60,   1
6: 252,  1, 24,   1, 132,    1
7:   1, 40,  1,  33,   1, 5460,  1
8: 240,  1, 44,   1, 936,    1, 12,    1
9:   1, 33,  1, 585,   1,    3,  1, 1020, 1
		

Crossrefs

Numerators in A287703.

Programs

Maple

T := (n, k) -> denom((-1)^(n+k)*binomial(n-1, k)*bernoulli(n+k)/(n+k)):
for n from 1 to 9 do seq(T(n, k), k=0..n-1) od;

Mathematica

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 *)

PARI

T(n, k) = denominator((-1)^n*binomial(n-1,k)*bernfrac(k+n)/(k+n));
tabl(nn) = for (n=1, nn, for (k=0, n-1, print1(T(n, k), ", ")); print); \\ Michel Marcus, Jul 28 2017