A307353 a(n) = Sum_{1<=i<=j<=k<=n} (i+j+k)!/(i!*j!*k!).
0, 6, 138, 2808, 59083, 1298797, 29538183, 688783509, 16365391557, 394523905488, 9621386549905, 236859066714283, 5876752842394018, 146774130963028054, 3686474939155802036, 93044751867415156290, 2358431594463240429469
Offset: 0
Keywords
Programs
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Mathematica
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 *) -
PARI
{a(n) = sum(i=1, n, sum(j=i, n, sum(k=j, n, (i+j+k)!/(i!*j!*k!))))}
Formula
a(n) ~ 3^(3*n + 13/2) / (832*Pi*n). - Vaclav Kotesovec, Apr 04 2019