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 A094250 #9 Aug 20 2023 10:50:08
%S A094250 1,1,3,1,3,7,1,3,8,15,1,3,9,22,31,1,3,10,31,63,63,1,3,11,42,117,185,
%T A094250 127,1,3,12,55,199,459,550,255,1,3,13,70,315,981,1825,1644,511,1,3,14,
%U A094250 87,471,1871,4888,7287,4925,1023,1,3,15,106,673,3273,11203,24420,29133,14767,2047
%N A094250 Array, A(n, k) = ((n+2)^(k+1) + (k+1)*n*(n+1) - 1)/(n+1)^2, read by antidiagonals.
%H A094250 G. C. Greubel, <a href="/A094250/b094250.txt">Antidiagonals n = 0..50, flattened</a>
%F A094250 A(n, k) = ((n+2)^(k+1) + (k+1)*n*(n+1) - 1)/(n+1)^2 (array).
%F A094250 T(n, k) = ((n-k+2)^(k+1) + (k+1)*(n-k)*(n-k+1) - 1)/(n-k+1)^2 (antidiagonals).
%F A094250 G.f. for row n: (1-(n+1)*x)/((1-(n+2)*x)*(1-x)^2).
%e A094250 Array, A(n, k), begins:
%e A094250 1, 3, 7, 15, 31, 63, 127, 255, 511, ... A000225;
%e A094250 1, 3, 8, 22, 63, 185, 550, 1644, 4925, ... A047926;
%e A094250 1, 3, 9, 31, 117, 459, 1825, 7287, 29133, ... A073724;
%e A094250 1, 3, 10, 42, 199, 981, 4888, 24420, 122077, ... A094195;
%e A094250 1, 3, 11, 55, 315, 1871, 11203, 67191, 403115, ... A094259;
%e A094250 1, 3, 12, 70, 471, 3273, 22882, 160140, 1120941, ...
%e A094250 Antidiagonals, T(n, k), begins as:
%e A094250 1;
%e A094250 1, 3;
%e A094250 1, 3, 7;
%e A094250 1, 3, 8, 15;
%e A094250 1, 3, 9, 22, 31;
%e A094250 1, 3, 10, 31, 63, 63;
%e A094250 1, 3, 11, 42, 117, 185, 127;
%e A094250 1, 3, 12, 55, 199, 459, 550, 255;
%e A094250 1, 3, 13, 70, 315, 981, 1825, 1644, 511;
%e A094250 1, 3, 14, 87, 471, 1871, 4888, 7287, 4925, 1023;
%t A094250 A094250[n_, k_]:= ((n-k+2)^(k+1) + (k+1)*(n-k)*(n-k+1) - 1)/(n-k+1)^2;
%t A094250 Table[A094250[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Aug 18 2023 *)
%o A094250 (Magma)
%o A094250 A094250:= func< n,k | ((n-k+2)^(k+1) + (k+1)*(n-k)*(n-k+1) - 1)/(n-k+1)^2 >;
%o A094250 [A094250(n,k): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Aug 18 2023
%o A094250 (SageMath)
%o A094250 def A094250(n, k): return ((n-k+2)^(k+1) + (k+1)*(n-k)*(n-k+1) - 1)/(n-k+1)^2
%o A094250 flatten([[A094250(n,k) for k in range(n+1)] for n in range(16)]) # _G. C. Greubel_, Aug 18 2023
%Y A094250 Rows are A000225, A047926, A073724, A094195, A094259.
%K A094250 nonn,tabl
%O A094250 0,3
%A A094250 _N. J. A. Sloane_, Jun 02 2004