A307358 a(n) = Sum_{0<=i<=j<=k<=n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).
1, -4, 72, -1345, 27886, -610558, 13861334, -322838475, 7663363513, -184598740512, 4498935186891, -110693299767349, 2745124008220296, -68532209858173364, 1720678086867077832, -43415209670536390089, 1100146390869600888470
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}], {j, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 04 2019 *) -
PARI
{a(n) = sum(i=0, n, sum(j=i, n, sum(k=j, n, (-1)^(i+j+k)*(i+j+k)!/(i!*j!*k!))))}
Formula
a(n) ~ (-1)^n * 3^(3*n + 13/2) / (1792*Pi*n). - Vaclav Kotesovec, Apr 04 2019