(PARI/GP): deriv(-eta(x)) 1 + 2*x - 5*x^4 - 7*x^6 + 12*x^11 + ... here: eta(x) = prod(n=1, \infty, 1-x^n) I get d/dx eta(x) = eta(x) / x * sum(n=1,\infty, -x^(n-1)/(1-x^n)) this appears to check with the comment Convolved with the partition numbers A000041 = sigma(n) prefaced with an 0: (0, 1, 3, 4, 7, 6, 12, 8, 15, 13,...).