A394506 Triangle read by rows: T(n,k) = numerator(binomial(1/n, k)) with 1 <= k <= n.

1, 1, -1, 1, -1, 5, 1, -3, 7, -77, 1, -2, 6, -21, 399, 1, -5, 55, -935, 4301, -124729, 1, -3, 13, -65, 351, -1989, 81549, 1, -7, 35, -805, 4991, -64883, 435643, -23960365, 1, -4, 68, -442, 3094, -68068, 515372, -3994133, 283583443, 1, -9, 57, -1653, 64467, -1052961, 8874957, -612372033, 5375265623, -478398640447

Offset

1,6

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

The triangle of the fractions begins:
  1/1;
  1/2,  -1/8;
  1/3,  -1/9,  5/81;
  1/4, -3/32, 7/128, -77/2048;
  1/5, -2/25, 6/125,  -21/625, 399/15625;
  ...

Mathematica

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

Crossrefs

Cf. A007318, A026741, A394507 (denominators).

First column gives A000012.

Right diagonal gives A364713.

Sequence in context: A214803 A225984 A074048 * A244350 A392318 A176321

Adjacent sequences: A394502 A394503 A394504 * A394507 A394508 A394509

Keyword

sign,easy,frac,tabl

Author

Stefano Spezia, Mar 22 2026

Status

approved