       Re: multinomials: a programming question

• To: mathgroup at smc.vnet.net
• Subject: [mg3948] Re: multinomials: a programming question
• From: Count Dracula <lk3a at kelvin.seas.virginia.edu>
• Date: Fri, 10 May 1996 03:32:54 -0400
• Organization: University of Virginia
• Sender: owner-wri-mathgroup at wolfram.com

```In Message-ID: <4menll\$jva at dragonfly.wolfram.com> Jack Goldberg

> I need to write the trinomial expansion
> out in terms of Sum.  Something like this:

> tri[a_,b_,c_,n_] := Sum[Multinomial[i,j,k]*a^i*b^j*c*k, ???]
> where  i+j+k = n.

In:= <<DiscreteMath`Combinatorica`

f[{a_, b_, c_}, {i_, j_, k_}] := Multinomial[i, j, k] a^i b^j c k

tri[x_List, n_Integer] := Apply[Plus, (f[x, #1] & ) /@ Compositions[n, 3]]

In:= tri[{a, b, c}, 3]

2                          2
Out= 3 c + 6 a c + 3 a  c + 6 b c + 6 a b c + 3 b  c

In:= tri[{1, 3, 5}, 4]

Out= 2500
--
___________________________________________________________________________________
Levent Kitis           lk3a at cars.mech.virginia.edu    lk3a at kelvin.seas.virginia.edu
University of Virginia Department of Mechanical, Aerospace, and Nuclear Engineering

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```

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