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 A334781 #9 May 18 2020 18:59:31
%S A334781 0,0,1,0,1,2,0,1,4,3,0,1,10,10,4,0,1,28,46,20,5,0,1,82,244,146,35,6,0,
%T A334781 1,244,1378,1244,371,56,7,0,1,730,8020,11378,4619,812,84,8,0,1,2188,
%U A334781 47386,108020,62003,13880,1596,120,9,0,1,6562,282124,1047386,867395,256484,35832,2892,165,10
%N A334781 Array read by antidiagonals: T(n,k) = Sum_{i=1..n} binomial(1+i,2)^k.
%H A334781 Andrew Howroyd, <a href="/A334781/b334781.txt">Table of n, a(n) for n = 0..1325</a>
%F A334781 T(n,k) = Sum_{i=0..2*(k-1)} A154283(k,i) * binomial(n+2+i, 2*k+i) for k > 0.
%e A334781 Array begins:
%e A334781 ===============================================================
%e A334781 n\k | 0 1 2 3 4 5 6 7
%e A334781 ----|----------------------------------------------------------
%e A334781 0 | 0 0 0 0 0 0 0 0 ...
%e A334781 1 | 1 1 1 1 1 1 1 1 ...
%e A334781 2 | 2 4 10 28 82 244 730 2188 ...
%e A334781 3 | 3 10 46 244 1378 8020 47386 282124 ...
%e A334781 4 | 4 20 146 1244 11378 108020 1047386 10282124 ...
%e A334781 5 | 5 35 371 4619 62003 867395 12438011 181141499 ...
%e A334781 6 | 6 56 812 13880 256484 4951496 98204132 1982230040 ...
%e A334781 7 | 7 84 1596 35832 871140 22161864 580094436 15475158552 ...
%e A334781 ...
%o A334781 (PARI) T(n,k) = {sum(i=1, n, binomial(1+i,2)^k)}
%Y A334781 Columns k=0..7 are A001477, A000292, A024166, A085438, A085439, A085440, A085441, A085442.
%Y A334781 Rows n=0..3 are A000004, A000012, A034472, A074508.
%Y A334781 Main diagonal is A249564(n > 0).
%Y A334781 Cf. A154283 (coefficients).
%K A334781 nonn,tabl
%O A334781 0,6
%A A334781 _Andrew Howroyd_, May 15 2020