[seqfan] Re: A class of partitions.

L. Edson Jeffery lejeffery2 at gmail.com
Mon Apr 29 00:08:45 CEST 2013


Wouter, William,

Thanks for your combined insight. Finding a generating function may be
impossible because of the restriction on the parts. But the number of
partitions of N for which no part is greater than k is equal to the number
of partitions of N with precisely k parts, N = 1, 2, ..., 1 <= k <= N. Then
apparently the number of partitions of 2*n+1 for which no part is greater
than n should be given by

a(n) = sum_{k=1,...,n} A008284(2*n+1,k)
     = coefficient of x^(2*n+1) in series expansion of
1/((1-x)*(1-x^2)*...*(1-x^n)),

unless I made a mistake.

It appears further that the series expansion of
x^(N-1)/((1-x)*(1-x^2)*...*(1-x^k))
generates column k of A008284. If true, then that generating function is
not included in the formula section of A008284.

Ed Jeffery

Re: http://oeis.org/A008284


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