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 A168518 #6 Apr 01 2022 09:14:53
%S A168518 1,1,1,1,12,1,1,51,51,1,1,170,514,170,1,1,521,3646,3646,521,1,1,1552,
%T A168518 22247,49472,22247,1552,1,1,4591,125565,534995,534995,125565,4591,1,1,
%U A168518 13590,677776,5058698,9506078,5058698,677776,13590,1,1,40341,3560448,43870968,140136690,140136690,43870968,3560448,40341,1
%N A168518 Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -4, b = 2, and c = 2, read by rows.
%H A168518 G. C. Greubel, <a href="/A168518/b168518.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A168518 G.f.: (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1 - x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -4, b = 2, and c = 2.
%F A168518 From _G. C. Greubel_, Mar 31 2022: (Start)
%F A168518 T(n, k) = (1/2)*( a*binomial(n,k) + sum( (-1)^(k-j)*(b*binomial(n+2, k-j)*(j+1)^(n+1) + 2*c*binomial(n+1,k-j)*(2*j+1)^n) for j in (0..k)) ), with a = -4, b = 2, and c = 2.
%F A168518 T(n, n-k) = T(n, k). (End)
%e A168518 Triangle begins as:
%e A168518 1;
%e A168518 1, 1;
%e A168518 1, 12, 1;
%e A168518 1, 51, 51, 1;
%e A168518 1, 170, 514, 170, 1;
%e A168518 1, 521, 3646, 3646, 521, 1;
%e A168518 1, 1552, 22247, 49472, 22247, 1552, 1;
%e A168518 1, 4591, 125565, 534995, 534995, 125565, 4591, 1;
%e A168518 1, 13590, 677776, 5058698, 9506078, 5058698, 677776, 13590, 1;
%e A168518 1, 40341, 3560448, 43870968, 140136690, 140136690, 43870968, 3560448, 40341, 1;
%t A168518 p[x_, n_, a_, b_, c_]= (1/2)*(a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi[x,-n-1,1] + c*2^(n+1)*(1-x)^(n+1)*LerchPhi[x,-n,1/2]);
%t A168518 Table[CoefficientList[p[x,n,-4,2,2], x], {n,0,10}]//Flatten (* modified by _G. C. Greubel_, Mar 31 2022 *)
%o A168518 (Sage)
%o A168518 def A168518(n,k,a,b,c): return (1/2)*( a*binomial(n,k) + sum( (-1)^(k-j)*(b*binomial(n+2, k-j)*(j+1)^(n+1) + 2*c*binomial(n+1,k-j)*(2*j+1)^n) for j in (0..k)) )
%o A168518 flatten([[A168518(n,k,-4,2,2) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 31 2022
%Y A168518 Cf. A142460, A155491, A155495, A157273, A166343.
%Y A168518 Cf. A168517, A168549, A168551, A168552.
%K A168518 nonn,tabl
%O A168518 0,5
%A A168518 _Roger L. Bagula_, Nov 28 2009
%E A168518 Edited by _G. C. Greubel_, Mar 31 2022