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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.
1
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
0,3
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).
EXAMPLE
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 ... |
| ... | ... ... ... ... ... ... ... ... |
+-----+--------------------------------------------------------------+
PROG
(PARI) T(n, k) = numerator(polylog(-n, 1/k));
matrix(7, 7, n, k, T(n-1, k+1)) \\ Michel Marcus, Aug 04 2024
CROSSREFS
Cf. A374896 (denominators).
Sequence in context: A322044 A010251 A051537 * A338797 A171999 A036038
KEYWORD
nonn,tabl,frac
AUTHOR
Mohammed Yaseen, Jul 22 2024
STATUS
approved