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I'm trying to compute the triple sum

Sum[1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}]

but Mathematica doesn't return
any value. What else can I do here? Thanks!

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Maybe because it does not have an exact values in terms of $\pi$, $e$ and other known constants or functions. N[Sum[1/(i! j! k!), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}]] computes fine and returns 0.122759. – m0nhawk Jan 21 at 13:18
Maybe NSum is sufficient in your case ? – b.gatessucks Jan 21 at 13:20
@m0nhawk: I'm sure that in the answer must also be the constant $e$. The triple sums also involves the hypergeometric function but this shouldn't be a problem, right? – Chris's sister Jan 21 at 13:21
@Chris'ssister: 1. It was just an assumption why it does not compute nothing. 2. That a function that gives the numerical value of expression, see N. – m0nhawk Jan 21 at 13:24
@m0nhawk: thank you very much for the explanations offered! – Chris's sister Jan 21 at 13:26
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