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Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 4x.
7

%I #21 Jun 12 2018 08:18:38

%S 4,-10,20,-60,204,-690,2340,-8160,29120,-104958,381300,-1397740,

%T 5162220,-19175130,71582716,-268431360,1010580540,-3817763040,

%U 14467258260,-54975528948,209430785460,-799645010850,3059510616420

%N Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 4x.

%H Seiichi Manyama, <a href="/A038065/b038065.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 + 4*x^k)/k. - _Ilya Gutkovskiy_, May 23 2017

%F a(n) ~ -(-1)^n * 4^n / n. - _Vaclav Kotesovec_, Jun 12 2018

%o (PARI) x='x+O('x^24); Vec(sum(k=1, 24, moebius(k)*log(1 + 4*x^k)/k)) \\ _Indranil Ghosh_, May 24 2017

%Y Cf. A038063, A038064, A038066, A038067, A038068, A038069, A038070.

%K sign

%O 1,1

%A _Christian G. Bower_, Jan 04 1999