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

%I #16 Jun 23 2018 15:25:47

%S 4,-6,20,-66,204,-670,2340,-8226,29120,-104754,381300,-1398410,

%T 5162220,-19172790,71582716,-268439586,1010580540,-3817733920,

%U 14467258260,-54975633702,209430785460,-799644629550,3059510616420

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

%H Seiichi Manyama, <a href="/A038069/b038069.txt">Table of n, a(n) for n = 1..1000</a>

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

%F Dirichlet convolution of A038065 with characteristic function of powers of 2.

%F a(n) = (1/n)*(-(-4)^n + Sum_{d<n and d|n} (-1)^(n/d)*d*a(d)). - _Seiichi Manyama_, Jun 23 2018

%Y Cf. A038063-A038070, A306158.

%K sign

%O 1,1

%A _Christian G. Bower_, Jan 04 1999