The total number of irreducible representations of S_n is the partition function p(n) (sequence A000041) and the number of irreducible representations of the symmetric group S_n that have odd degree is given in A059867 so a(n) = A000041(n) - A059867(n) for n >= 1
EXAMPLE
a(3) = 1 because the degrees of the irreducible representations of S_3 are 1,1,2.