A185694 Eigensequence for the Moebius mu triangle A152904.

1, -1, 2, -2, 3, -2, 1, 4, -10, 22, -36, 56, -72, 84, -71, 22, 99, -311, 654, -1122, 1702, -2267, 2611, -2312, 795, 2789, -9352, 19802, -34442, 52436, -70521, 81869, -74248, 29099, 79012, -279732, 600894, -1054809, 1616669, -2190772, 2567994

Offset: 0

Author

Paul Barry, Feb 10 2011

Keywords

• sign

Comments

First column of the inverse of the number triangle T(n,k)=if(kA152904(n-1,k), if(k=n,1,0)).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008683, A073776, A300663.

Programs

Haskell

a185694 n = a185694_list !! (n-1)
a185694_list = 1 : f [1] where
   f xs = y : f (y : xs) where
          y = sum $ zipWith (*) xs $ map negate a008683_list
-- Reinhard Zumkeller, Nov 03 2015

Mathematica

nmax = 50; CoefficientList[Series[1/(1 + Sum[MoebiusMu[k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 30 2024 *)

Formula

G.f.: 1 / (1 + Sum_{k>=1} mu(k)*x^k). - Ilya Gutkovskiy, Oct 02 2022