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.
%I A345394 #10 Aug 29 2022 09:54:43
%S A345394 1,2,1,5,6,1,14,37,14,1,41,234,165,30,1,122,1513,1826,613,62,1,365,
%T A345394 9966,19689,10770,2085,126,1,1094,66637,210134,175465,55154,6757,254,
%U A345394 1,3281,450834,2236365,2741670,1287657,260274,21285,510,1,9842,3077713,23819306,41809933,27930182,8420713,1167026,65893,1022,1
%N A345394 Array read by ascending antidiagonals: A(n, k) = n!*[x^n] Li(-k, 1 - exp(-4*x))/(4*sinh(x)), where Li(n, z) is the polylogarithm function.
%H A345394 Beáta Bényi and Toshiki Matsusaka, <a href="https://arxiv.org/abs/2106.05585">Extensions of the combinatorics of poly-Bernoulli numbers</a>, arXiv:2106.05585 [math.CO], 2021. See p. 9.
%H A345394 Komatsu, Takao <a href="https://doi.org/10.1007/s10998-017-0199-7">Complementary Euler numbers</a>. Period. Math. Hung. 75, No. 2, 302-314 (2017).
%H A345394 Takao Komatsu, <a href="https://arxiv.org/abs/1806.05515">On poly-Euler numbers of the second kind</a>, arXiv:1806.05515 [math.NT], 2018.
%e A345394 n\k| 0 1 2 3 4 ...
%e A345394 ---+----------------------------------
%e A345394 0 | 1 1 1 1 1 ...
%e A345394 1 | 2 6 14 30 62 ...
%e A345394 2 | 5 37 165 613 2085 ...
%e A345394 3 | 14 234 1826 10770 55154 ...
%e A345394 4 | 41 1513 19689 175465 1287657 ...
%e A345394 ...
%t A345394 A[n_,k_]:=n!Coefficient[Series[PolyLog[-k,1-Exp[-4t]]/(4Sinh[t]),{t,0,n}],t,n]; Flatten[Table[A[n-k,k],{n,0,9},{k,0,n}]]
%Y A345394 Cf. A000012 (n = 0), A007051 (k = 0), A081188 (k = 1), A305861 (n = 2), A305862 (n = 3), A305863 (n = 4), A316526 (n = 5), A345393.
%K A345394 nonn,tabl
%O A345394 0,2
%A A345394 _Stefano Spezia_, Jun 17 2021