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 A345393 #10 Jun 30 2021 19:56:29
%S A345393 0,1,0,4,1,0,13,12,1,0,40,109,28,1,0,121,888,493,60,1,0,364,6841,7192,
%T A345393 1837,124,1,0,1093,51012,95161,42840,6253,252,1,0,3280,372709,1189108,
%U A345393 865081,220120,20269,508,1,0,9841,2687088,14331493,16022100,6396601,1040088,63853,1020,1,0
%N 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.
%H A345393 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 A345393 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 A345393 n\k| 0 1 2 3 4 ...
%e A345393 ---+------------------------------
%e A345393 0 | 0 0 0 0 0 ...
%e A345393 1 | 1 1 1 1 1 ...
%e A345393 2 | 4 12 28 60 124 ...
%e A345393 3 | 13 109 493 1837 6253 ...
%e A345393 4 | 40 888 7192 42840 220120 ...
%e A345393 ...
%t A345393 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}]]
%Y A345393 Cf. A000004 (n = 0), A000012 (n = 1), A003462 (k = 0), A081200 (k = 1), A345394.
%K A345393 nonn,tabl
%O A345393 0,4
%A A345393 _Stefano Spezia_, Jun 17 2021