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%I #11 Jun 15 2023 07:39:57
%S 1,-3,11,-23,36,-49,85,-143,176,-188,287,-433,456,-479,726,-959,970,
%T -1024,1331,-1748,1866,-1741,2301,-3153,2961,-2824,3830,-4559,4496,
%U -4514,5457,-6943,6842,-6174,7890,-9844,9140,-8553,11126,-13348,12342,-11998,14191,-16941
%N Expansion of Sum_{k>=1} x^k/(1 + x^k)^4.
%H Seiichi Manyama, <a href="/A320901/b320901.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=1} (-1)^(k+1)*A000292(k)*x^k/(1 - x^k).
%F a(n) = Sum_{d|n} (-1)^(d+1)*d*(d + 1)*(d + 2)/6.
%F a(n) = (4*A000593(n) + 6*A050999(n) + 2*A051000(n) - 2*A000203(n) - 3*A001157(n) - A001158(n))/6.
%p seq(coeff(series(add(x^k/(1+x^k)^4,k=1..n),x,n+1), x, n), n = 1 .. 45); # _Muniru A Asiru_, Oct 23 2018
%t nmax = 44; Rest[CoefficientList[Series[Sum[x^k/(1 + x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]]
%t Table[Sum[(-1)^(d + 1) d (d + 1) (d + 2)/6, {d, Divisors[n]}], {n, 44}]
%Y Cf. A000203, A000292, A000593, A001157, A001158, A002129, A050999, A051000, A059358, A320900.
%Y Cf. A363598, A363616, A363617, A363631.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Oct 23 2018
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