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%I #15 Apr 22 2019 07:05:44
%S 1,1,3,3,3,7,-3,13,-5,-7,49,-97,93,155,-997,2893,-5989,9007,-7121,
%T -10805,63305,-169375,321137,-418503,152653,1142657,-4565939,11378145,
%U -21893565,32887315,-33140953,-1985517,113177979,-348817177,734074637,-1210600023
%N Inverse binomial transform of A156616.
%H Vaclav Kotesovec, <a href="/A294505/b294505.txt">Table of n, a(n) for n = 0..3000</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A156616(k).
%F G.f.: (1/(1 + x))*exp(Sum_{k>=1} (sigma_2(2*k) - sigma_2(k))*x^k/(2*k*(1 + x)^k)). - _Ilya Gutkovskiy_, Oct 15 2018
%t nmax = 40; s = CoefficientList[Series[Product[((1+x^k)/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[(-1)^(n-k) * Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]
%Y Cf. A156616, A294501, A294503, A294504.
%K sign
%O 0,3
%A _Vaclav Kotesovec_, Nov 01 2017
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