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%I #4 Aug 11 2021 21:38:31
%S 1,-1,0,-2,1,-3,1,-4,4,-6,2,-7,8,-8,5,-13,13,-14,9,-15,19,-21,12,-22,
%T 32,-26,18,-36,33,-37,31,-38,57,-48,32,-56,66,-57,44,-74,83,-75,65,
%U -76,100,-102,68,-103,140,-108,94,-136,140,-137,119,-149,193,-174,125,-175,228,-176,161,-224,256
%N a(1) = 1; a(n+1) = -Sum_{k=1..n} a(floor(n/k)).
%F G.f. A(x) satisfies: A(x) = x - (x/(1 - x)) * Sum_{k>=1} (1 - x^k) * A(x^k).
%t a[1] = 1; a[n_] := a[n] = -Sum[a[Floor[(n - 1)/k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 65}]
%t nmax = 65; A[_] = 0; Do[A[x_] = x - (x/(1 - x)) Sum[(1 - x^k) A[x^k], {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A078346, A309288, A328967.
%K sign
%O 1,4
%A _Ilya Gutkovskiy_, Aug 11 2021
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