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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 (list; table; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A345390 A345391 A345392 * A345394 A345395 A345396 KEYWORD nonn,tabl AUTHOR Stefano Spezia, Jun 17 2021 STATUS approved

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Last modified January 25 06:44 EST 2022. Contains 350565 sequences. (Running on oeis4.)