A307369 - OEIS

%I #12 May 20 2021 04:44:36

%S 0,0,3,-51,1059,-23090,522721,-12147685,287854454,-6924261148,

%T 168559758222,-4143307764311,102667574424349,-2561308686267644,

%U 64269232404321663,-1620744761933019015,41050609554433557263,-1043736712034774976330,26628094150076388266301

%N a(n) = -Sum_{0<=i<j<k<=n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).

%t 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 (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 Cf. A306409, A306432, A307358.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 05 2019