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 A117435 #8 Jun 02 2021 22:16:47
%S A117435 1,0,1,-4,0,1,0,-12,0,1,16,0,-24,0,1,0,80,0,-40,0,1,-64,0,240,0,-60,0,
%T A117435 1,0,-448,0,560,0,-84,0,1,256,0,-1792,0,1120,0,-112,0,1,0,2304,0,
%U A117435 -5376,0,2016,0,-144,0,1,-1024,0,11520,0,-13440,0,3360,0,-180,0,1
%N A117435 Triangle related to exp(x)*cos(2*x).
%C A117435 Diagonals correspond to rows of A117438.
%H A117435 G. C. Greubel, <a href="/A117435/b117435.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A117435 Number triangle whose k-th column has e.g.f. (x^k/k!)*cos(2x);
%F A117435 T(n, k) = binomial(n,k) * (-4)^((n-k)/2) * (1+(-1)^(n-k))/2.
%F A117435 Sum_{k=0..n} T(n, k) = A006495(n).
%F A117435 Sum_{k=0..floor(n/2)} T(n-k, k) = i^n * ((1+(-1)^n)/2) * (2*floor(n/2) + 1). - _G. C. Greubel_, Jun 01 2021
%e A117435 Triangle begins:
%e A117435 1;
%e A117435 0, 1;
%e A117435 -4, 0, 1;
%e A117435 0, -12, 0, 1;
%e A117435 16, 0, -24, 0, 1;
%e A117435 0, 80, 0, -40, 0, 1;
%e A117435 -64, 0, 240, 0, -60, 0, 1;
%t A117435 T[n_,k_]:= Binomial[n,k]*(2*I)^(n-k)*(1+(-1)^(n+k))/2;
%t A117435 Table[T[n,k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 01 2021 *)
%o A117435 (Sage) flatten([[binomial(n,k)*(2*i)^(n-k)*(1+(-1)^(n+k))/2 for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 01 2021
%Y A117435 Cf. A006495 (row sums), A117411, A117436 (inverse), A117438.
%K A117435 easy,sign,tabl
%O A117435 0,4
%A A117435 _Paul Barry_, Mar 16 2006