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 A306432 #30 May 17 2019 02:39:13
%S A306432 0,0,3,77,1777,41088,964199,22962721,553886872,13504654074,
%T A306432 332253097450,8237141855085,205552200503455,5158397884289338,
%U A306432 130087682458168777,3294763277704155587,83764781257030939439,2136808562574516060202,54674217200832983666877
%N A306432 a(n) = Sum_{0<=i<j<k<=n} (i+j+k)!/(i!*j!*k!).
%H A306432 Robert Israel, <a href="/A306432/b306432.txt">Table of n, a(n) for n = 0..700</a>
%F A306432 a(n) ~ 3^(3*n + 7/2) / (832*Pi*n). - _Vaclav Kotesovec_, Apr 05 2019
%p A306432 g:= proc(n) local i,j;
%p A306432 add(add((i+j+n)!/(i!*j!*n!),j=i+1..n-1),i=0..n-2)
%p A306432 end proc:
%p A306432 ListTools:-PartialSums(map(g,[$0..30])); # _Robert Israel_, May 16 2019
%t A306432 Table[Sum[Sum[Sum[(i + j + k)!/(i!*j!*k!), {i, 0, j-1}], {j, 0, k-1}], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 05 2019 *)
%o A306432 (PARI) {a(n) = sum(i=0, n, sum(j=i+1, n, sum(k=j+1, n, (i+j+k)!/(i!*j!*k!))))}
%Y A306432 Cf. A057552, A307352.
%K A306432 nonn
%O A306432 0,3
%A A306432 _Seiichi Manyama_, Apr 05 2019