A374896 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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