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 A307353 #10 Apr 04 2019 05:41:00
%S A307353 0,6,138,2808,59083,1298797,29538183,688783509,16365391557,
%T A307353 394523905488,9621386549905,236859066714283,5876752842394018,
%U A307353 146774130963028054,3686474939155802036,93044751867415156290,2358431594463240429469
%N A307353 a(n) = Sum_{1<=i<=j<=k<=n} (i+j+k)!/(i!*j!*k!).
%F A307353 a(n) ~ 3^(3*n + 13/2) / (832*Pi*n). - _Vaclav Kotesovec_, Apr 04 2019
%t A307353 Table[Sum[Sum[Sum[(i+j+k)!/(i!*j!*k!), {i, 1, j}], {j, 1, k}], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 04 2019 *)
%o A307353 (PARI) {a(n) = sum(i=1, n, sum(j=i, n, sum(k=j, n, (i+j+k)!/(i!*j!*k!))))}
%Y A307353 Cf. A120279, A144511, A144660, A307352.
%K A307353 nonn
%O A307353 0,2
%A A307353 _Seiichi Manyama_, Apr 03 2019