OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Product_{n>=1} 1 + x^(2*n)/(1 - x^n)^3.
EXAMPLE
a(4)=7. In order to designate two summands of each size, the multiplicity of each summand must be at least two. For n=4 we consider only the partitions 2+2 and 1+1+1+1. In the first case there is 1 way and in the second case there are 6 ways. 1 + 6 = 7.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+add(b(n-i*j, i-1)*binomial(j, 2), j=2..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..50); # Alois P. Heinz, Mar 19 2015
MATHEMATICA
nn = 40; CoefficientList[Series[Product[1 + x^(2 n)/(1 - x^n)^3, {n, 1, nn}], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Mar 19 2015
STATUS
approved