%N Partial sums of number of functors of degree n from free Abelian groups to Abelian groups A007322.
%C Partial sums of partial sums of number of matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n (A120733). Partial sums of dimensions of the graded components of the Hopf algebra MQSym (Matrix quasi-symmetric functions). a(2) = 7 is the only prime through a(18).
%F a(n) = SUM[i=1..n]] SUM[r>=0,s>=0] binomial(r*s+i-1,i)/2^(r+s+2).
%e a(3) = 1 + 6 + 39 = 46.
%Y Cf. A007322, A120733.
%A _Jonathan Vos Post_, Dec 31 2010