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How can I write in Mathematica an expression like this?

$$\sum_{k=1}^n {_{k}F_{k}} (1,1,\dots,1; \,2,2,\dots,2; \,z) ~,$$

where ${_{p}F_{q}}$ is the generalized hypergeometric function.

My problem is that I don't know how to use variable number of arguments, which depends on a parameter.

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Thanks to ConstantArray[], not much effort is needed:

mysum[n_Integer, z_] :=
   Sum[HypergeometricPFQ[ConstantArray[1, k], ConstantArray[2, k], z], {k, 1, n}]

Test:

mysum[3, z]
   (-1 + E^z)/z + HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, z] +
   (-EulerGamma - Gamma[0, -z] - Log[-z])/z
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  • 2
    $\begingroup$ Table[1, k] and Table[2, k] are slightly more compact. $\endgroup$ – Bob Hanlon Aug 15 '15 at 16:14

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