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 A225532 #13 Mar 30 2022 06:13:11
%S A225532 1,1,1,1,26,1,1,27,27,1,1,120,1192,120,1,1,121,1312,1312,121,1,1,502,
%T A225532 14609,88736,14609,502,1,1,503,15111,103345,103345,15111,503,1,1,2036,
%U A225532 152638,2205524,9890752,2205524,152638,2036,1,1,2037,154674,2358162,12096276,12096276,2358162,154674,2037,1
%N A225532 Triangle T(n, k) = abs(A225483(n/2, k)) if (n mod 2 = 0), otherwise abs(A225482((n-1)/2, k) - A225483((n-1)/2, k-1)), read by rows.
%H A225532 G. C. Greubel, <a href="/A225532/b225532.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A225532 From _G. C. Greubel_, Mar 29 2022: (Start)
%F A225532 T(n, k) = abs(A225483(n/2, k)) if (n mod 2 = 0), otherwise abs(A225482((n-1)/2, k) - A225483((n-1)/2, k-1)).
%F A225532 T(n, n-k) = T(n, k). (End)
%e A225532 Triangle begins:
%e A225532 1;
%e A225532 1, 1;
%e A225532 1, 26, 1;
%e A225532 1, 27, 27, 1;
%e A225532 1, 120, 1192, 120, 1;
%e A225532 1, 121, 1312, 1312, 121, 1;
%e A225532 1, 502, 14609, 88736, 14609, 502, 1;
%e A225532 1, 503, 15111, 103345, 103345, 15111, 503, 1;
%t A225532 (* First program *)
%t A225532 Needs["Combinatorica`"];
%t A225532 p[n_, x_]:= p[n,x]= Sum[If[i==Floor[n/2] && Mod[n, 2]==0, 0, If[i<=Floor[n/2], (-1)^i*Eulerian[n+1,i]*x^i, (-1)^(n-i+1)*Eulerian[n+1,i]*x^i]], {i,0,n}]/(1 - x^2);
%t A225532 q[n_, x_]= If[Mod[n,2]==0, (1-x)*p[n/2,x], p[(n+1)/2,x]];
%t A225532 Table[Abs[CoefficientList[q[(4*n +(-1)^n +5)/2, x], x]], {n,0,12}]//Flatten (* modified by _G. C. Greubel_, Mar 29 2022 *)
%t A225532 (* Second program *)
%t A225532 A008292[n_, k_]:= A008292[n, k]= Sum[(-1)^j*(k-j)^n*Binomial[n+1,j], {j,0,k}];
%t A225532 f[n_, k_]:= f[n, k]= If[k==0 || k==n, 1, If[k<=Floor[n/2], f[n,k-1] + (-1)^k*A008292[n+2,k+1], f[n,n-k]]]; (* f=A159041 *)
%t A225532 A225483[n_, k_]:= Sum[(-1)^(k-j)*f[2*n+1,j], {j,0,k}];
%t A225532 T[n_, k_]:= If[Mod[n,2]==0, A225483[n/2, k], A225483[(n-1)/2, k] - A225483[(n - 1)/2, k-1] ]//Abs;
%t A225532 Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 29 2022 *)
%o A225532 (Sage)
%o A225532 def A008292(n, k): return sum( (-1)^j*(k-j)^n*binomial(n+1, j) for j in (0..k) )
%o A225532 @CachedFunction
%o A225532 def f(n, k): # A159041
%o A225532 if (k==0 or k==n): return 1
%o A225532 elif (k <= (n//2)): return f(n, k-1) + (-1)^k*A008292(n+2, k+1)
%o A225532 else: return f(n, n-k)
%o A225532 def A225483(n,k): return sum( (-1)^(k-j)*f(2*n+1,j) for j in (0..k) )
%o A225532 @CachedFunction
%o A225532 def A225532(n,k):
%o A225532 if (n%2==0): return abs(A225483(n/2, k))
%o A225532 else: return abs( A225483((n-1)/2, k) - A225483((n-1)/2, k-1) )
%o A225532 flatten([[A225532(n, k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 29 2022
%Y A225532 Cf. A008292, A159041, A171692, A204621, A225483.
%K A225532 nonn,tabl
%O A225532 0,5
%A A225532 _Roger L. Bagula_, May 09 2013
%E A225532 Edited by _G. C. Greubel_, Mar 29 2022