OFFSET
0,11
COMMENTS
The g.f. for "number of k's" is (1/2)*(x^k/(1+x^k))*(Product_{n>=1} 1 + x^n) - (1/2)*(x^k/(1-x^k))*(Product_{n>=1} 1 - x^n).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
a(12) = 3 because the partitions in question are: 10+2, 6+3+2+1, 5+4+2+1.
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], EvenQ[Length[#]]&&Length[#] == Length[ Union[#]]&&MemberQ[#, 2]&]], {n, 0, 50}] (* Harvey P. Dale, Dec 09 2014 *)
PROG
(PARI) seq(n)={my(A=O(x^(n-1))); Vec(x*(eta(x^2 + A)/(eta(x + A)*(1+x^2)) - eta(x + A)/(1-x^2))/2, -(n+1))} \\ Andrew Howroyd, May 01 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Feb 20 2014
EXTENSIONS
Terms a(51) and beyond from Andrew Howroyd, May 01 2020
STATUS
approved