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 A306444 #26 Sep 08 2022 08:46:21
%S A306444 1,1,1,1,2,1,1,5,7,1,1,14,66,30,1,1,42,715,1144,143,1,1,132,8398,
%T A306444 49742,22610,728,1,1,429,104006,2340135,3991995,482885,3876,1,1,1430,
%U A306444 1337220,115997970,757398510,347993910,10855425,21318,1
%N A306444 A(n,k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2), square array A(n,k) read by antidiagonals, for n >= 0, k >= 0.
%H A306444 Seiichi Manyama, <a href="/A306444/b306444.txt">Antidiagonals n = 0..81, flattened</a>
%e A306444 Square array begins:
%e A306444 1, 1, 1, 1, 1, ...
%e A306444 1, 2, 5, 14, 42, ...
%e A306444 1, 7, 66, 715, 8398, ...
%e A306444 1, 30, 1144, 49742, 2340135, ...
%e A306444 1, 143, 22610, 3991995, 757398510, ...
%e A306444 1, 728, 482885, 347993910, 267058714626, ...
%e A306444 1, 3876, 10855425, 32018897274, 99543581789652, ...
%t A306444 A[n_, k_]:= Binomial[(2*k+1)*n+2, k*n+1]/((2*k+1)*n+2); Table[A[k, n-k], {n,0,12}, {k,0,n}] (* _G. C. Greubel_, Feb 16 2019 *)
%o A306444 (PARI) {A(n,k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2)};
%o A306444 for(n=0,12, for(k=0,n, print1(A(k,n-k), ", "))) \\ _G. C. Greubel_, Feb 16 2019
%o A306444 (Magma) [[Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2): k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Feb 16 2019
%o A306444 (Sage) [[binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Feb 16 2019
%o A306444 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) ))); # _G. C. Greubel_, Feb 16 2019
%Y A306444 Columns 0-1 give A000012, A006013.
%Y A306444 Rows 0-5 give A000012, A000108(n+1), A065097(n+1), A265101, A265102, A265103.
%K A306444 nonn,tabl
%O A306444 0,5
%A A306444 _Seiichi Manyama_, Feb 15 2019