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 A168523 #6 Mar 20 2022 02:19:21
%S A168523 1,1,1,1,8,1,1,31,31,1,1,98,290,98,1,1,289,1974,1974,289,1,1,836,
%T A168523 11719,25944,11719,836,1,1,2419,64929,275307,275307,64929,2419,1,1,
%U A168523 7046,346192,2573466,4831134,2573466,346192,7046,1,1,20677,1804144,22163080,70723522,70723522,22163080,1804144,20677,1
%N A168523 Triangle of coefficients of g.f. a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -1, b = 1, c = 1.
%H A168523 G. C. Greubel, <a href="/A168523/b168523.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A168523 From _G. C. Greubel_, Mar 19 2022: (Start)
%F A168523 G.f.: a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -1, b = 1, c = 1.
%F A168523 T(n, n-k) = T(n, k). (End)
%e A168523 Triangle begins as:
%e A168523 1;
%e A168523 1, 1;
%e A168523 1, 8, 1;
%e A168523 1, 31, 31, 1;
%e A168523 1, 98, 290, 98, 1;
%e A168523 1, 289, 1974, 1974, 289, 1;
%e A168523 1, 836, 11719, 25944, 11719, 836, 1;
%e A168523 1, 2419, 64929, 275307, 275307, 64929, 2419, 1;
%e A168523 1, 7046, 346192, 2573466, 4831134, 2573466, 346192, 7046, 1;
%e A168523 1, 20677, 1804144, 22163080, 70723522, 70723522, 22163080, 1804144, 20677, 1;
%t A168523 T[n_, a_, b_, c_]:= CoefficientList[Series[a*(1+x)^n + b*(1-x)^(n+2)* PolyLog[-n-1, x]/x + 2^n*c*(1-x)^(n+1)*LerchPhi[x, -n, 1/2], {x,0,30}], x];
%t A168523 Table[T[n,-1,1,1], {n, 0, 12}]//Flatten (* modified by _G. C. Greubel_, Mar 19 2022 *)
%o A168523 (Sage)
%o A168523 m=12
%o A168523 def LerchPhi(x,s,a): return sum( x^j/(j+a)^s for j in (0..3*m) )
%o A168523 def p(n,x,a,b,c): return a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2)
%o A168523 def T(n,k,a,b,c): return ( p(n,x,a,b,c) ).series(x, n+1).list()[k]
%o A168523 flatten([[T(n,k,-1,1,1) for k in (0..n)] for n in (0..m)]) # _G. C. Greubel_, Mar 19 2022
%Y A168523 Cf. A142458, A142459.
%Y A168523 Cf. A168524, A168525.
%K A168523 nonn,tabl
%O A168523 0,5
%A A168523 _Roger L. Bagula_, Nov 28 2009
%E A168523 Edited by _G. C. Greubel_, Mar 19 2022