login
Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 5x.
6

%I #22 Jun 12 2018 08:14:12

%S 5,-15,40,-150,624,-2620,11160,-48750,217000,-976872,4438920,

%T -20343700,93900240,-435970980,2034504992,-9536718750,44878791360,

%U -211927733500,1003867701480,-4768371093720,22706531339280

%N Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 5x.

%H Seiichi Manyama, <a href="/A038066/b038066.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Euler transform</a>

%F G.f.: Sum_{k>=1} mu(k)*log(1 + 5*x^k)/k. - _Ilya Gutkovskiy_, May 23 2017

%F a(n) ~ -(-1)^n * 5^n / n. - _Vaclav Kotesovec_, Jun 12 2018

%o (PARI) x='x+O('x^22); Vec(sum(k=1, 22, moebius(k)*log(1 + 5*x^k)/k)) \\ _Indranil Ghosh_, May 24 2017

%Y Cf. A038063, A038064, A038065, A038067, A038068, A038069, A038070.

%K sign

%O 1,1

%A _Christian G. Bower_, Jan 04 1999