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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.

A143505 Triangle of coefficients of the polynomials x^(n - 1)*A(n,x + 1/x), where A(n,x) are the Eulerian polynomials of A008292.

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%I A143505 #14 Feb 16 2025 08:33:08
%S A143505 1,1,1,1,1,4,3,4,1,1,11,14,23,14,11,1,1,26,70,104,139,104,70,26,1,1,
%T A143505 57,307,530,973,947,973,530,307,57,1,1,120,1197,3016,5970,8568,9549,
%U A143505 8568,5970,3016,1197,120,1,1,247,4300,17101,37105,70474,90069,107241,90069
%N A143505 Triangle of coefficients of the polynomials x^(n - 1)*A(n,x + 1/x), where A(n,x) are the Eulerian polynomials of A008292.
%C A143505 Row sums yield A000670 (without leading 1).
%H A143505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>
%F A143505 Row n is generated by the polynomial (1 - x - 1/x)^(n + 1)*x^(n - 1)*Li(-n, x + 1/x)/(x + 1/x), where Li(n, z) is the polylogarithm function.
%F A143505 E.g.f.: (exp(x*y) - exp((1 + x^2)*y))/(x*exp((1 + x^2)*y) - (1 + x^2)*exp(x*y)). - _Franck Maminirina Ramaharo_, Oct 25 2018
%e A143505 Triangle begins:
%e A143505    1;
%e A143505    1,  1,   1;
%e A143505    1,  4,   3,   4,   1;
%e A143505    1, 11,  14,  23,  14,  11,   1;
%e A143505    1, 26,  70, 104, 139, 104,  70,  26,   1;
%e A143505    1, 57, 307, 530, 973, 947, 973, 530, 307, 57, 1;
%e A143505     ... reformatted. - _Franck Maminirina Ramaharo_, Oct 25 2018
%t A143505 Table[CoefficientList[FullSimplify[ExpandAll[(1 - x - 1/x)^(n + 1)*x^(n - 1)*PolyLog[-n, x + 1/x]/(x + 1/x)]], x], {n, 1, 10}]//Flatten
%Y A143505 Compare with A141720.
%Y A143505 Cf. A008292.
%Y A143505 Cf. A143506, A143507.
%K A143505 nonn,tabf
%O A143505 1,6
%A A143505 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 25 2008
%E A143505 Edited and new name by _Franck Maminirina Ramaharo_, Oct 25 2018