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A345393
Array read by ascending antidiagonals: A(n, k) = n!*[x^(n-1)] Li(-k, 1 - exp(-4*x))/(4*x*cosh(x)), where Li(n, z) is the polylogarithm function.
1
0, 1, 0, 4, 1, 0, 13, 12, 1, 0, 40, 109, 28, 1, 0, 121, 888, 493, 60, 1, 0, 364, 6841, 7192, 1837, 124, 1, 0, 1093, 51012, 95161, 42840, 6253, 252, 1, 0, 3280, 372709, 1189108, 865081, 220120, 20269, 508, 1, 0, 9841, 2687088, 14331493, 16022100, 6396601, 1040088, 63853, 1020, 1, 0
OFFSET
0,4
LINKS
Beáta Bényi and Toshiki Matsusaka, Extensions of the combinatorics of poly-Bernoulli numbers, arXiv:2106.05585 [math.CO], 2021. See p. 9.
Takao Komatsu, On poly-Euler numbers of the second kind, arXiv:1806.05515 [math.NT], 2018.
EXAMPLE
n\k| 0 1 2 3 4 ...
---+------------------------------
0 | 0 0 0 0 0 ...
1 | 1 1 1 1 1 ...
2 | 4 12 28 60 124 ...
3 | 13 109 493 1837 6253 ...
4 | 40 888 7192 42840 220120 ...
...
MATHEMATICA
A[n_, k_]:=n!Coefficient[Series[PolyLog[-k, 1-Exp[-4x]]/(4x Cosh[x]), {x, 0, n}], x, n-1]; Flatten[Table[A[n-k, k], {n, 0, 9}, {k, 0, n}]]
CROSSREFS
Cf. A000004 (n = 0), A000012 (n = 1), A003462 (k = 0), A081200 (k = 1), A345394.
Sequence in context: A060638 A244125 A007789 * A081114 A069018 A156811
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jun 17 2021
STATUS
approved