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 A304330 #17 Aug 03 2025 10:22:19
%S A304330 1,0,1,0,1,12,0,1,60,360,0,1,252,5040,20160,0,1,1020,52920,604800,
%T A304330 1814400,0,1,4092,506880,12640320,99792000,239500800,0,1,16380,
%U A304330 4684680,230630400,3632428800,21794572800,43589145600,0,1,65532,42653520,3952428480,111567456000,1264085222400,6102480384000,10461394944000
%N A304330 T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n), triangle read by rows, n >= 0 and 0 <= k <= n.
%H A304330 José L. Cereceda, <a href="https://arxiv.org/abs/2405.05268">Sums of powers of integers and the sequence A304330</a>, arXiv:2405.05268 [math.GM], 2024.
%e A304330 Triangle starts:
%e A304330 [0] 1;
%e A304330 [1] 0, 1;
%e A304330 [2] 0, 1, 12;
%e A304330 [3] 0, 1, 60, 360;
%e A304330 [4] 0, 1, 252, 5040, 20160;
%e A304330 [5] 0, 1, 1020, 52920, 604800, 1814400;
%e A304330 [6] 0, 1, 4092, 506880, 12640320, 99792000, 239500800;
%e A304330 [7] 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600;
%p A304330 T := (n, k) -> add((-1)^j*binomial(2*k,j)*(k-j)^(2*n), j=0..k):
%p A304330 for n from 0 to 8 do seq(T(n, k), k=0..n) od;
%o A304330 (PARI) T(n, k) = sum(j=0, k, (-1)^j*binomial(2*k, j)*(k - j)^(2*n)); \\ _Michel Marcus_, Aug 03 2025
%Y A304330 Row sums are A100872, T(n,2) = A058896, T(n,n) = A002674, T(n,n-1)= A091032.
%Y A304330 Cf. A304334, A304336.
%K A304330 nonn,tabl
%O A304330 0,6
%A A304330 _Peter Luschny_, May 11 2018