cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A374895 Array read by falling antidiagonals: T(n,k) = numerator(Sum_{x>0} (x^n)/(k^x)); n >= 0 and k >= 2.

Original entry on oeis.org

1, 1, 2, 1, 3, 6, 1, 4, 3, 26, 1, 5, 20, 33, 150, 1, 6, 15, 44, 15, 1082, 1, 7, 42, 115, 380, 273, 9366, 1, 8, 7, 366, 285, 4108, 1491, 94586, 1, 9, 72, 91, 4074, 3535, 17780, 38001, 1091670, 1, 10, 45, 776, 70, 11334, 26355, 269348, 17295, 14174522, 1, 11, 110, 531, 10440, 2149, 189714, 458555, 4663060, 566733, 204495126
Offset: 0

Views

Author

Mohammed Yaseen, Jul 22 2024

Keywords

Examples

			Array begins:
+-----+--------------------------------------------------------------+
| n\k |       2     3       4       5        6      7         8  ... |
+-----+--------------------------------------------------------------+
|  0  |       1     1       1       1        1      1         1  ... |
|  1  |       2     3       4       5        6      7         8  ... |
|  2  |       6     3      20      15       42      7        72  ... |
|  3  |      26    33      44     115      366     91       776  ... |
|  4  |     150    15     380     285     4074     70     10440  ... |
|  5  |    1082   273    4108    3535    11334   2149    174728  ... |
|  6  |    9366  1491   17780   26355   189714   3311   3525192  ... |
|  7  |   94586 38001  269348  458555  3706518 285929  11870648  ... |
|  8  | 1091670 17295 4663060 1139685 82749954 220430 319735800  ... |
| ... |     ...   ...     ...     ...      ...    ...       ...  ... |
+-----+--------------------------------------------------------------+

Crossrefs

Cf. A374896 (denominators).
Cf. A000629, A008292, A121376, A276805.

Programs

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

Formula

T(n,k) = numerator(polylog(-n, 1/k)).
T(n,k) = numerator(1/(k-1)^(n+1) * Sum_{m=1..n} A008292(n,m)*k^m).
T(0,k) = 1.
T(1,k) = k.
T(2,k) = A276805(k-1).
T(n,2) = A000629(n).
T(n,n) = A121376(n).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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