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 A168549 #6 Apr 01 2022 09:15:00
%S A168549 1,1,1,1,3,1,1,67,67,1,1,435,1596,435,1,1,1951,16476,16476,1951,1,1,
%T A168549 7383,123243,282258,123243,7383,1,1,25507,783537,3435627,3435627,
%U A168549 783537,25507,1,1,83595,4543678,34677285,65518690,34677285,4543678,83595,1,1,265351,24934378,312192718,1002545920,1002545920,312192718,24934378,265351,1
%N A168549 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 = 31, b = -59, and c = 15, read by rows.
%H A168549 G. C. Greubel, <a href="/A168549/b168549.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A168549 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 = 31, b = -59, and c = 15.
%F A168549 From _G. C. Greubel_, Mar 31 2022: (Start)
%F A168549 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 = 31, b = -59, and c = 15.
%F A168549 T(n, n-k) = T(n, k). (End)
%e A168549 Triangle begins as:
%e A168549 1;
%e A168549 1, 1;
%e A168549 1, 3, 1;
%e A168549 1, 67, 67, 1;
%e A168549 1, 435, 1596, 435, 1;
%e A168549 1, 1951, 16476, 16476, 1951, 1;
%e A168549 1, 7383, 123243, 282258, 123243, 7383, 1;
%e A168549 1, 25507, 783537, 3435627, 3435627, 783537, 25507, 1;
%e A168549 1, 83595, 4543678, 34677285, 65518690, 34677285, 4543678, 83595, 1;
%t A168549 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 A168549 Table[CoefficientList[p[x,n,31,-59,15], x], {n,0,10}]//Flatten (* modified by _G. C. Greubel_, Mar 31 2022 *)
%o A168549 (Sage)
%o A168549 def A168549(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 A168549 flatten([[A168549(n,k,31,-59,15) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 31 2022
%Y A168549 Cf. A001263. A168517, A168518, A168551, A168552.
%K A168549 nonn,tabl
%O A168549 0,5
%A A168549 _Roger L. Bagula_, Nov 29 2009
%E A168549 Edited by _G. C. Greubel_, Mar 31 2022