|
%I #11 Sep 15 2019 10:54:27
%S 0,1,-2,5,-4,4,-6,17,-14,6,-10,28,-12,8,-36,49,-16,13,-18,46,-52,12,
%T -22,100,-44,14,-68,64,-28,24,-30,129,-84,18,-92,121,-36,20,-100,166,
%U -40,32,-42,100,-192,24,-46,292,-90,31,-132,118,-52,40,-148,232,-148,30,-58,264
%N Expansion of Sum_{k>=1} k * x^(2*k) / (1 + x^k)^2.
%H Seiichi Manyama, <a href="/A325941/b325941.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=2} (-1)^k * (k - 1) * x^k / (1 - x^k)^2.
%F a(n) = Sum_{d|n} (-1)^(n/d) * (n - d).
%F a(n) = A000593(n) - n * A048272(n).
%t nmax = 60; CoefficientList[Series[Sum[k x^(2 k)/(1 + x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t Table[Sum[(-1)^(n/d) (n - d), {d, Divisors[n]}], {n, 1, 60}]
%o (PARI) {a(n) = sumdiv(n, d, (-1)^(n/d)*(n-d))} \\ _Seiichi Manyama_, Sep 14 2019
%Y Cf. A000593, A048272, A094471, A143520.
%K sign
%O 1,3
%A _Ilya Gutkovskiy_, Sep 09 2019
|
