login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..54.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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