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 A061176 #10 Apr 06 2021 23:09:26
%S A061176 1,1,-1,1,-1,1,1,0,0,-1,1,2,-5,2,1,1,5,-15,15,-5,-1,1,9,-30,41,-30,9,
%T A061176 1,1,14,-49,77,-77,49,-14,-1,1,20,-70,112,-125,112,-70,20,1,1,27,-90,
%U A061176 126,-117,117,-126,90,-27,-1,1,35,-105,90,45,-131,45,90,-105,35,1
%N A061176 Coefficients of polynomials ( (1 -x +sqrt(x))^n + (1 -x -sqrt(x))^n )/2.
%C A061176 The row polynomial pFe(k+1, x) = Sum_{j=0..k+1} T(k+1, j)*x^j is the numerator of the g.f. for the k-th column sequence of A060920, the even part of the bisected Fibonacci triangle.
%H A061176 G. C. Greubel, <a href="/A061176/b061176.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A061176 T(n, k) = coefficients of x^k of ((1-x+sqrt(x))^n + (1-x-sqrt(x))^n)/2.
%F A061176 T(n, k) = Sum_{j=0..k} (-1)^(k-j)*binomial(n, 2*j)*binomial(n-2*j, k-j), if 0 <= k <= floor(n/2) and T(n, k) = (-1)^n*T(n, n-k) if floor(n/2) < k <= n, otherwise 0.
%F A061176 Sum_{k=0..n} T(n, k) = A059841(n) = (1 + (-1)^n)/2. - _G. C. Greubel_, Apr 06 2021
%e A061176 The first few polynomials are:
%e A061176 pFe(0,x) = 1.
%e A061176 pFe(1,x) = 1 - x.
%e A061176 pFe(2,x) = 1 - x + x^2.
%e A061176 pFe(3,x) = 1 - 0*x + 0*x^2 - x^3.
%e A061176 pFe(4,x) = 1 + 2*x - 5*x^2 + 2*x^3 + x^4.
%e A061176 Number triangle begins as:
%e A061176 1;
%e A061176 1, -1;
%e A061176 1, -1, 1;
%e A061176 1, 0, 0, -1;
%e A061176 1, 2, -5, 2, 1;
%e A061176 1, 5, -15, 15, -5, -1;
%e A061176 1, 9, -30, 41, -30, 9, 1;
%e A061176 1, 14, -49, 77, -77, 49, -14, -1;
%e A061176 1, 20, -70, 112, -125, 112, -70, 20, 1;
%t A061176 T[n_, k_]:= Sum[(-1)^(k+j)*Binomial[n, 2*j]*Binomial[n-2*j, k-j], {j,0,k}];
%t A061176 Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Apr 06 2021 *)
%o A061176 (Magma)
%o A061176 A061176:= func< n,k | (&+[(-1)^(k+j)*Binomial(n,2*j)*Binomial(n-2*j,k-j): j in [0..k]]) >;
%o A061176 [A061176(n,k): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Apr 06 2021
%o A061176 (Sage)
%o A061176 def A061176(n,k): return sum((-1)^(k+j)*binomial(n,2*j)*binomial(n-2*j,k-j) for j in (0..k))
%o A061176 flatten([[A061176(n,k) for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Apr 06 2021
%Y A061176 Cf. A059841, A060920, A061177 (companion triangle), A180957.
%K A061176 sign,easy,tabl
%O A061176 0,12
%A A061176 _Wolfdieter Lang_, Apr 20 2001