[seqfan] GF for A147843?

Joerg Arndt arndt at jjj.de
Mon Mar 15 14:54:17 CET 2010


(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,...).






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