A374896 Array read by falling antidiagonals: T(n,k) = denominator(Sum_{x>0} (x^n)/(k^x)); n >= 0 and k >= 2.

1, 2, 1, 3, 4, 1, 4, 9, 2, 1, 5, 16, 27, 8, 1, 6, 25, 32, 27, 1, 1, 7, 36, 125, 128, 81, 4, 1, 8, 49, 27, 625, 128, 243, 4, 1, 9, 64, 343, 216, 3125, 512, 243, 16, 1, 10, 81, 256, 2401, 81, 3125, 1024, 729, 1, 1, 11, 100, 729, 2048, 16807, 972, 15625, 4096, 2187, 4, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = denominator(polylog(-n, 1/k)).

T(n,k) = denominator(1/(k-1)^(n+1) * Sum_{m=1..n} A008292(n,m)*k^m).

T(0,k) = k-1.

T(1,k) = (k-1)^2.

T(2,k) = A277542(k-1).

T(n,2) = 1.

T(n,n) = A121985(n).

Example

Array begins:
+-----+-----------------------------------------------+
| n\k |   2    3     4    5      6     7       8  ... |
+-----+-----------------------------------------------+
|  0  |   1    2     3    4      5     6       7  ... |
|  1  |   1    4     9   16     25    36      49  ... |
|  2  |   1    2    27   32    125    27     343  ... |
|  3  |   1    8    27  128    625   216    2401  ... |
|  4  |   1    1    81  128   3125    81   16807  ... |
|  5  |   1    4   243  512   3125   972  117649  ... |
|  6  |   1    4   243 1024  15625   486  823543  ... |
|  7  |   1   16   729 4096  78125 11664  823543  ... |
|  8  |   1    1  2187 2048 390625  2187 5764801  ... |
| ... | ...  ...   ...  ...    ...   ...     ...  ... |
+-----+-----------------------------------------------+

Prog

(PARI) T(n, k) = denominator(polylog(-n, 1/k));
matrix(7, 7, n, k, T(n-1, k+1)) \\ Michel Marcus, Aug 04 2024

Crossrefs

Cf. A374895 (numerators).

Cf. A008292, A121985, A277542.

Sequence in context: A247358 A297224 A180383 * A133807 A325001 A093375

Adjacent sequences: A374893 A374894 A374895 * A374897 A374898 A374899

Keyword

nonn,tabl,frac

Author

Mohammed Yaseen, Aug 03 2024

Status

approved