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 A176078 #10 Sep 08 2022 08:45:52
%S A176078 1,1,1,1,19,1,1,161,161,1,1,1051,2451,1051,1,1,6049,24949,24949,6049,
%T A176078 1,1,32341,206977,368677,206977,32341,1,1,164737,1510081,4200769,
%U A176078 4200769,1510081,164737,1,1,810811,10077211,40347451,63050131,40347451,10077211,810811,1
%N A176078 Triangle, read by rows, T(n, k) = (2*n)!/((n-k)! * k!)^2 - (2*n)!/(n!)^2 + 1.
%C A176078 Row sums are: {1, 2, 21, 324, 4555, 61998, 847315, 11751176, 165521079, 2363418210, 34132747231, ...}.
%H A176078 G. C. Greubel, <a href="/A176078/b176078.txt">Rows n = 0..100 of triangle, flattened</a>
%F A176078 T(n, k) = (2*n)!/((n-k)! * k!)^2 - (2*n)!/(n!)^2 + 1.
%F A176078 T(n, k) = binomial(2*n,n)*( binomial(n,k)^2 - 1) + 1. - _G. C. Greubel_, Nov 27 2019
%e A176078 Triangle begins as:
%e A176078 1;
%e A176078 1, 1;
%e A176078 1, 19, 1;
%e A176078 1, 161, 161, 1;
%e A176078 1, 1051, 2451, 1051, 1;
%e A176078 1, 6049, 24949, 24949, 6049, 1;
%e A176078 1, 32341, 206977, 368677, 206977, 32341, 1;
%e A176078 1, 164737, 1510081, 4200769, 4200769, 1510081, 164737, 1;
%p A176078 b:=binomial; T(n,k):=b(2*n,n)*(b(n,k)^2 -1)+1; seq(seq(T(n,k), k=0..n), n=0..10); # _G. C. Greubel_, Nov 27 2019
%t A176078 T[n_, k_] = (2*n)!/((n-k)!*k!)^2 - (2*n)!/(n!)^2 + 1; Table[T[n, k], {n, 0, 10}, (k, 0, n)]//Flatten
%o A176078 (PARI) b=binomial; T(n,k) = b(2*n,n)*(b(n,k)^2 -1)+1; \\ _G. C. Greubel_, Nov 27 2019
%o A176078 (Magma) B:=Binomial; [B(2*n,n)*(B(n,k)^2 -1)+1: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Nov 27 2019
%o A176078 (Sage) b=binomial; [[b(2*n,n)*(b(n,k)^2 -1)+1 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Nov 27 2019
%o A176078 (GAP) B:=Binomial;; Flat(List([0..10], n-> List([0..n], k-> B(2*n,n)*(B(n,k)^2 -1)+1 ))); # _G. C. Greubel_, Nov 27 2019
%Y A176078 Cf. A141902, A000984
%K A176078 nonn,tabl
%O A176078 0,5
%A A176078 _Roger L. Bagula_, Apr 08 2010