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%I #17 May 29 2021 02:01:45
%S 1,-1,4,-6,6,-3,8,-22,20,0,12,-44,14,7,72,-95,18,-10,20,-71,142,33,24,
%T -399,152,52,248,-57,30,-121,32,-679,398,102,828,-685,38,133,600,
%U -1568,42,-140,44,318,2864,207,48,-5858,1766,-751,1192,831,54,348,4424,-3979,1598,348,60
%N a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+n/d-1, d).
%H Seiichi Manyama, <a href="/A344777/b344777.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k >= 1} x^k/(1 + x^k)^(k+1).
%F If p is prime, a(p) = 1 + (-1)^(p-1) * p.
%t a[n_] := DivisorSum[n, (-1)^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 60] (* _Amiram Eldar_, May 28 2021 *)
%o (PARI) a(n) = sumdiv(n, d, (-1)^(n/d-1)*binomial(d+n/d-1, d));
%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1+x^k)^(k+1)))
%Y Cf. A081543, A217670, A338682.
%K sign
%O 1,3
%A _Seiichi Manyama_, May 28 2021
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