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 A169656 #9 Sep 08 2022 08:45:49
%S A169656 -1,4,1,-36,-18,-1,576,432,48,1,-14400,-14400,-2400,-100,-1,518400,
%T A169656 648000,144000,9000,180,1,-25401600,-38102400,-10584000,-882000,
%U A169656 -26460,-294,-1,1625702400,2844979200,948326400,98784000,3951360,65856,448,1
%N A169656 Triangle, read by rows, T(n, k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1).
%C A169656 Row sums are: {-1, 5, -55, 1057, -31301, 1319581, -74996755, 5521809665, -510921831817, 58003632177301, ...}.
%H A169656 G. C. Greubel, <a href="/A169656/b169656.txt">Rows n = 1..100 of triangle, flattened</a>
%F A169656 T(n, k) = (-1)^n * (n!/k!)^2 * binomial(n-1, k-1).
%e A169656 Triangle begins as:
%e A169656 -1;
%e A169656 4, 1;
%e A169656 -36, -18, -1;
%e A169656 576, 432, 48, 1;
%e A169656 -14400, -14400, -2400, -100, -1;
%e A169656 518400, 648000, 144000, 9000, 180, 1;
%e A169656 -25401600, -38102400, -10584000, -882000, -26460, -294, -1;
%p A169656 seq(seq( (-1)^n*(n!/k!)^2*binomial(n-1, k-1), k=1..n), n=1..10); # _G. C. Greubel_, Nov 28 2019
%t A169656 T[n_, k_]:= (-1)^n*(n!/k!)^2*Binomial[n-1, k-1]; Table[T[n, k], {n,10}, {k,n}]//Flatten
%o A169656 (PARI) T(n,k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1); \\ _G. C. Greubel_, Nov 28 2019
%o A169656 (Magma) F:=Factorial; [(-1)^n*(F(n)/F(k))^2*Binomial(n-1, k-1): k in [1..n], n in [1..10]]; // _G. C. Greubel_, Nov 28 2019
%o A169656 (Sage) f=factorial; [[(-1)^n*(f(n)/f(k))^2*binomial(n-1, k-1) for k in (1..n)] for n in (1..10)] # _G. C. Greubel_, Nov 28 2019
%o A169656 (GAP) F:=Factorial;; Flat(List([1..10], n-> List([1..n], k-> (-1)^n*(F(n)/F(k) )^2*Binomial(n-1, k-1) ))); # _G. C. Greubel_, Nov 28 2019
%Y A169656 Cf. A008297.
%K A169656 sign,tabl
%O A169656 1,2
%A A169656 _Roger L. Bagula_, Apr 05 2010
%E A169656 Edited by _G. C. Greubel_, Nov 28 2019