A307369
a(n) = -Sum_{0<=i
0, 0, 3, -51, 1059, -23090, 522721, -12147685, 287854454, -6924261148, 168559758222, -4143307764311, 102667574424349, -2561308686267644, 64269232404321663, -1620744761933019015, 41050609554433557263, -1043736712034774976330, 26628094150076388266301
Offset: 0
Keywords
Programs
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Mathematica
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 *) -
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!))))}