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%I #14 Apr 22 2019 07:05:33
%S 1,0,1,1,-3,10,-23,48,-92,171,-321,626,-1265,2576,-5099,9478,-15925,
%T 22617,-21816,-8506,121659,-436121,1204710,-2962759,6860591,-15427559,
%U 34323613,-76269455,169591278,-376162414,827819644,-1798045927,3839392935,-8041078328
%N Inverse binomial transform of A026007.
%H Vaclav Kotesovec, <a href="/A294503/b294503.txt">Table of n, a(n) for n = 0..3000</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A026007(k).
%F G.f.: (1/(1 + x))*Product_{k>=1} (1 + x^k/(1 + x)^k)^k. - _Ilya Gutkovskiy_, Aug 20 2018
%t nmax = 40; s = CoefficientList[Series[Product[(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. A026007, A294501, A294502, A294505.
%K sign
%O 0,5
%A _Vaclav Kotesovec_, Nov 01 2017
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