OFFSET
0,4
COMMENTS
Number of partitions of n having no part that appears exactly twice.
Infinite convolution product of [1,1,0,1,1,1,1,1,1,1] aerated n-1 times. I.e., [1,1,0,1,1,1,1,1,1,1] * [1,0,1,0,0,0,1,0,1,0] * [1,0,0,1,0,0,0,0,0,1] * ... - Mats Granvik, Gary W. Adamson, Aug 07 2009
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Product_{j>=1} (1-x^(2j)+x^(3j))/(1-x^j).
G.f. for the number of partitions of n having no part that appears exactly m times is Product_{k>0} (1/(1-x^k)-x^(m*k)).
EXAMPLE
a(4) = 3 because we have [4],[3,1] and [1,1,1,1] (the partitions [2,2] and [2,1,1] do not qualify since each of them has a doubleton).
MAPLE
h:=product((1-x^(2*j)+x^(3*j))/(1-x^j), j=1..60): hser:=series(h, x=0, 60): seq(coeff(hser, x, n), n=0..56);
MATHEMATICA
nn=48; CoefficientList[Series[Product[1/(1-x^i)-x^(2i), {i, 1, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 30 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch and Vladeta Jovovic, Feb 20 2006
STATUS
approved