[seqfan] Re: A question about partitions

[William Keith]

Neil:

     Does this suffice?

G.f. of A003056: (1-x)^(-1)*Sum(n>=1, x^(n*(n+1)/2)).  G.f. of A001227:
Sum_{k >= 1} x^(k*(k+1)/2)/(1-x^k). Partitions of this type are of the form
(k+j, k+j-1, k+j-2, ..., k) + (1,1,1,...,0,0), with the number of 1s being
somewhere from 1 to j-1.  The g.f. of such partitions is thus Sum(n>=1,
x^((n*(n+1)/2)+1)) * (1+x+...x^(n-2)) * (1-x^n)^(-1) , which is seen to be
the difference of the previous two g.f.s.

(The g.f. also goes in the formula line, right?)

Best,
William