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 A245300 #11 Apr 01 2021 02:43:11
%S A245300 0,1,4,3,7,12,6,11,17,24,10,16,23,31,40,15,22,30,39,49,60,21,29,38,48,
%T A245300 59,71,84,28,37,47,58,70,83,97,112,36,46,57,69,82,96,111,127,144,45,
%U A245300 56,68,81,95,110,126,143,161,180,55,67,80,94,109,125,142,160,179,199,220
%N A245300 Triangle T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n, read by rows.
%H A245300 Reinhard Zumkeller, <a href="/A245300/b245300.txt">Rows n = 0..125 of triangle, flattened</a>
%F A245300 T(n, 0) = A000217(n).
%F A245300 T(n, n) = A046092(n).
%F A245300 T(2*n, n) = A062725(n) (central terms).
%F A245300 Sum_{k=0..n} T(n, k) = A245301(n).
%F A245300 From _G. C. Greubel_, Apr 01 2021: (Start)
%F A245300 T(n, 1) = A000124(n+1) = A134869(n+1), n >= 1.
%F A245300 T(n, 2) = A152948(n+4), n >= 2.
%F A245300 T(n, 3) = A152950(n+4), n >= 3.
%F A245300 T(n, 4) = A145018(n+5), n >= 4.
%F A245300 T(n, 5) = A167499(n+4), n >= 5.
%F A245300 T(n, 6) = A166136(n+5), n >= 6.
%F A245300 T(n, 7) = A167487(n+6), n >= 7.
%F A245300 T(n, n-1) = A056220(n), n >= 1.
%F A245300 T(n, n-2) = A142463(n-1), n >= 2.
%F A245300 T(n, n-3) = A054000(n-1), n >= 3.
%F A245300 T(n, n-4) = A090288(n-3), n >= 4.
%F A245300 T(n, n-5) = A268581(n-4), n >= 5.
%F A245300 T(n, n-6) = A059993(n-4), n >= 6.
%F A245300 T(n, n-7) = (-1)*A147973(n), n >= 7.
%F A245300 T(n, n-8) = A139570(n-5), n >= 8.
%F A245300 T(n, n-9) = A271625(n-5), n >= 9.
%F A245300 T(n, n-10) = A222182(n-4), n >= 10.
%F A245300 T(2*n, n-1) = A081270(n-1), n >= 1.
%F A245300 T(2*n, n+1) = A117625(n+1), n >= 1. (End)
%e A245300 First rows and their row sums (A245301):
%e A245300 0 0;
%e A245300 1, 4 5;
%e A245300 3, 7, 12 22;
%e A245300 6, 11, 17, 24 58;
%e A245300 10, 16, 23, 31, 40 120;
%e A245300 15, 22, 30, 39, 49, 60 215;
%e A245300 21, 29, 38, 48, 59, 71, 84 350;
%e A245300 28, 37, 47, 58, 70, 83, 97, 112 532;
%e A245300 36, 46, 57, 69, 82, 96, 111, 127, 144 768;
%e A245300 45, 56, 68, 81, 95, 110, 126, 143, 161, 180 1065;
%e A245300 55, 67, 80, 94, 109, 125, 142, 160, 179, 199, 220 1430;
%e A245300 66, 79, 93, 108, 124, 141, 159, 178, 198, 219, 241, 264 1870;
%e A245300 78, 92, 107, 123, 140, 158, 177, 197, 218, 240, 263, 287, 312 2392.
%t A245300 Table[k + Binomial[n+k+1,2], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Apr 01 2021 *)
%o A245300 (Haskell)
%o A245300 a245300 n k = (n + k) * (n + k + 1) `div` 2 + k
%o A245300 a245300_row n = map (a245300 n) [0..n]
%o A245300 a245300_tabl = map a245300_row [0..]
%o A245300 a245300_list = concat a245300_tabl
%o A245300 (Magma) [k + Binomial(n+k+1,2): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Apr 01 2021
%o A245300 (Sage) flatten([[k + binomial(n+k+1,2) for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Apr 01 2021
%Y A245300 Cf. A000217, A046092, A062725, A245301.
%K A245300 nonn,tabl
%O A245300 0,3
%A A245300 _Reinhard Zumkeller_, Jul 17 2014