Finite Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg43967] Finite Sum
• From: Ratna Bandila <choppalaks at yahoo.com>
• Date: Thu, 16 Oct 2003 04:16:01 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
I am unable to find the closed-form expression for
Sum[1/(m1!*m2!*m3!)^2],where m1+m2+m3=n

Mathematica does gives the result for
Sum[1/(m1!*m2!)^2],where m1+m2=n
as
(4^n*Gamma[n+(1/2)])/(Sqrt[pi]*Gamma[n+1]^3])
It also gives the closed-form formula for
Sum[1/(m1!*m2!*m3!)],where m1+m2+m3=n
Sum[1/(m1!*m2!*m3!*m4!)],where m1+m2+m3+m4=n
Sum[1/(m1!*m2!*m3!*m4!*m5!)],where m1+m2+m3+m4+m5=n
....and so on.

Kindly help if anyone has come across the expression.

Thanks
Ratna

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```

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