A394506 - OEIS

%I #7 Mar 26 2026 22:30:13

%S 1,1,-1,1,-1,5,1,-3,7,-77,1,-2,6,-21,399,1,-5,55,-935,4301,-124729,1,

%T -3,13,-65,351,-1989,81549,1,-7,35,-805,4991,-64883,435643,-23960365,

%U 1,-4,68,-442,3094,-68068,515372,-3994133,283583443,1,-9,57,-1653,64467,-1052961,8874957,-612372033,5375265623,-478398640447

%N Triangle read by rows: T(n,k) = numerator(binomial(1/n, k)) with 1 <= k <= n.

%F T(n,2) = - A026741(n-1) for n > 1.

%e The triangle of the fractions begins:

%e   1/1;

%e   1/2,  -1/8;

%e   1/3,  -1/9,  5/81;

%e   1/4, -3/32, 7/128, -77/2048;

%e   1/5, -2/25, 6/125,  -21/625, 399/15625;

%e   ...

%t T[n_,k_]:=Numerator[Binomial[1/n,k]]; Table[T[n,k],{n,10},{k,n}]//Flatten

%Y Cf. A007318, A026741, A394507 (denominators).

%Y First column gives A000012.

%Y Right diagonal gives A364713.

%K sign,easy,frac,tabl

%O 1,6

%A _Stefano Spezia_, Mar 22 2026