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 A144660 #17 Aug 22 2022 11:29:13
%S A144660 1,16,271,5248,110251,2435200,55621567,1301226496,30992872483,
%T A144660 748574130016,18283414868863,450657134765056,11192820128307871,
%U A144660 279787295456009728,7032532242167190271,177611430242835570688,4504491083159761986451,114662734697313744041248
%N A144660 a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} (i+j+k)!/(i!*j!*k!).
%H A144660 Seiichi Manyama, <a href="/A144660/b144660.txt">Table of n, a(n) for n = 0..100</a>
%H A144660 Vidunas, Raimundas <a href="https://doi.org/10.1007/s00026-017-0344-2">Counting derangements and Nash equilibria</a> Ann. Comb. 21, No. 1, 131-152 (2017).
%F A144660 From _Vaclav Kotesovec_, Apr 02 2019: (Start)
%F A144660 Recurrence: n^2*(2*n + 1)*(91*n^4 - 478*n^3 + 917*n^2 - 755*n + 222)*a(n) = 3*(2*n - 3)*(3*n - 5)*(3*n - 4)*(91*n^4 - 114*n^3 + 29*n^2 + 9*n - 3)*a(n-1) + n^2*(2*n + 1)*(91*n^4 - 478*n^3 + 917*n^2 - 755*n + 222)*a(n-2) - 3*(2*n - 3)*(3*n - 5)*(3*n - 4)*(91*n^4 - 114*n^3 + 29*n^2 + 9*n - 3)*a(n-3).
%F A144660 a(n) ~ 3^(3*n + 7/2) / (16*Pi*n). (End)
%p A144660 f:=n->add( add( add( (i+j+k)!/(i!*j!*k!), i=0..n),j=0..n),k=0..n); [seq(f(n),n=0..20)];
%t A144660 Table[Sum[(i + j + k)!/(i!*j!*k!), {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 02 2019 *)
%t A144660 Table[Sum[(1 + k + 2*n)! * HypergeometricPFQ[{1, -1 - k - n, -n}, {-1 - k - 2*n, -k - n}, 1] / ((1 + k + n)*k!*n!^2), {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 04 2019 *)
%o A144660 (PARI) {a(n) = sum(i=0, n, sum(j=0, n, sum(k=0, n, (i+j+k)!/(i!*j!*k!))))} \\ _Seiichi Manyama_, Apr 02 2019
%Y A144660 Cf. A030662, A144661, A307318. This sum is very close to that in A144511.
%K A144660 nonn
%O A144660 0,2
%A A144660 _N. J. A. Sloane_, Jan 31 2009, Feb 01 2009