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 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