[seqfan] checking a sequence before submission

David Newman davidsnewman at gmail.com
Mon Dec 13 16:37:25 CET 2010

Hi Sequence Fans,

     I'd like someone to check a sequence for me before I submit it,
having had the unpleasant experience of submitting an incorrect
sequence in the past.

     For a given positive integer, n, let S_n be the set of partitions
of n into distinct parts where the number of parts is maximal for that
n.  For example, for n=6, the set S_6 consists of just one such
partition S_6={1,2,3}.  Similarly, for n=7, S_7={1,2,4}, But for n=8,
S_8 will contain two partitions S_8= { {1,2,5}, {1,3,4} }.

     Now form the sum 1+ x/(1-x) + x^2/(1-x^2) + x^3/ ( ( 1-x)
(1-x^2)) + x^4/ ( ( 1-x) (1-x^3) ) +  x^5/  ( (1-x) (1-x^4) ) + x^5 (
( 1-x^2) (1-x^3)) + x^6/ ( ( 1-x) (1-x^2) (1-x^3)) + ...

whose general term is x^n divided by the product
(1-x^(p_1))...(1-x^(p_i))  where  the p's  come from the partitions in

The sequence is the sequence of coefficients of this sum.

The numbers that I've gotten are

If anyone is willing to do the calculations I can make the Mathematica
program which I used available to them .

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