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 A307369 #12 May 20 2021 04:44:36
%S A307369 0,0,3,-51,1059,-23090,522721,-12147685,287854454,-6924261148,
%T A307369 168559758222,-4143307764311,102667574424349,-2561308686267644,
%U A307369 64269232404321663,-1620744761933019015,41050609554433557263,-1043736712034774976330,26628094150076388266301
%N A307369 a(n) = -Sum_{0<=i<j<k<=n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).
%t A307369 Table[-Sum[Sum[Sum[(-1)^(i+j+k) * (i + j + k)!/(i!*j!*k!), {i, 0, j-1}], {j, 0, k-1}], {k, 0, n}], {n, 0, 20}] (* _Amiram Eldar_, May 20 2021 *)
%o A307369 (PARI) {a(n) = -sum(i=0, n, sum(j=i+1, n, sum(k=j+1, n, (-1)^(i+j+k)*(i+j+k)!/(i!*j!*k!))))}
%Y A307369 Cf. A306409, A306432, A307358.
%K A307369 sign
%O A307369 0,3
%A A307369 _Seiichi Manyama_, Apr 05 2019