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Article: Expansion of [x.sup.n] in Smarandache terms of permutations.

Article from:
Smarandache Notions Journal
Article date:
January 1, 2000
Author:
Copyright

ABSTRACT:

DEFINITION of SMARANDACHE TERM

Consider the expansion of [x.sup.n] as follows

[x.sup.n] = [b.sub.(n,1)] x + [b.sub.(n,2)] [x(x-1) + [b.sub.(n,3)] [x.sub.(x-1)(x-2) + ... + b(n,n)] [sup.x][P.sub.n]--(9.1)

We define [b.sub.(n,r)] x(x-1)(x-2) ... (x-r+1)(x-r) as the rth SMARANDACHE TERM in the above expansion of [x.sup.n].

In the present note we study the coefficients [b.sub.(n,r)].of the the rth SMARANDACHE TERM in such an expansion. We are encountered with fascinating coincidences.

DISCUSSION:

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