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A185694 Eigensequence for the Moebius mu triangle A152904.

%I A185694 #18 Nov 30 2024 11:03:30
%S A185694 1,-1,2,-2,3,-2,1,4,-10,22,-36,56,-72,84,-71,22,99,-311,654,-1122,
%T A185694 1702,-2267,2611,-2312,795,2789,-9352,19802,-34442,52436,-70521,81869,
%U A185694 -74248,29099,79012,-279732,600894,-1054809,1616669,-2190772,2567994
%N A185694 Eigensequence for the Moebius mu triangle A152904.
%C A185694 First column of the inverse of the number triangle T(n,k)=if(k<n, -A152904(n-1,k), if(k=n,1,0)).
%H A185694 Reinhard Zumkeller, <a href="/A185694/b185694.txt">Table of n, a(n) for n = 0..1000</a>
%F A185694 G.f.: 1 / (1 + Sum_{k>=1} mu(k)*x^k). - _Ilya Gutkovskiy_, Oct 02 2022
%t A185694 nmax = 50; CoefficientList[Series[1/(1 + Sum[MoebiusMu[k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 30 2024 *)
%o A185694 (Haskell)
%o A185694 a185694 n = a185694_list !! (n-1)
%o A185694 a185694_list = 1 : f [1] where
%o A185694    f xs = y : f (y : xs) where
%o A185694           y = sum $ zipWith (*) xs $ map negate a008683_list
%o A185694 -- _Reinhard Zumkeller_, Nov 03 2015
%Y A185694 Cf. A008683, A073776, A300663.
%K A185694 sign
%O A185694 0,3
%A A185694 _Paul Barry_, Feb 10 2011