A394507 Triangle read by rows: T(n,k) = denominator(binomial(1/n, k)) with 1 <= k <= n.

1, 2, 8, 3, 9, 81, 4, 32, 128, 2048, 5, 25, 125, 625, 15625, 6, 72, 1296, 31104, 186624, 6718464, 7, 49, 343, 2401, 16807, 117649, 5764801, 8, 128, 1024, 32768, 262144, 4194304, 33554432, 2147483648, 9, 81, 2187, 19683, 177147, 4782969, 43046721, 387420489, 31381059609

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..11325 (rows 1..150, flattened).

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_]:=Denominator[Binomial[1/n, k]]; Table[T[n, k], {n, 9}, {k, n}]//Flatten

Prog

(Magma) T:= function(n, k) r:= &*[(RationalField()!1/n-j):j in [0..k-1]] / Factorial(k);
return Denominator(r); end function; &cat[[T(n, k):k in [1..n]]:n in [1..9]]; // Vincenzo Librandi, Mar 23 2026

Crossrefs

Cf. A007318, A394506 (numerators).

Columns k=1..2 give A000027, A181900.

Right diagonal gives A145921.

Sequence in context: A082236 A337822 A362269 * A262027 A328487 A388982

Adjacent sequences: A394503 A394504 A394506 * A394508 A394509 A394510

Keyword

nonn,easy,frac,tabl

Author

Stefano Spezia, Mar 22 2026

Status

approved