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A073777
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a(n) = Sum_{k=1..n} -A068341(k+1)*a(n-k), a(0)=1.
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3
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1, 2, 5, 10, 22, 42, 85, 162, 314, 588, 1113, 2066, 3847, 7080, 13036, 23824, 43504, 79048, 143441, 259376, 468313, 843352, 1516515, 2721470, 4877165, 8726118, 15593224, 27826634, 49602226, 88316198, 157089101, 279137436, 495566701, 879034448, 1557979289
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OFFSET
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0,2
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COMMENTS
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Recurrence relation involves the convolution of the Moebius function (A068341).
Radius of convergence of A(x) is r=0.5802946238073267...
Related limits are limit_{n->infinity} a(n) r^n/n = 0.406...(?) and limit_{n->infinity} a(n+1)/a(n) = 1.723262561763844...
This sequence is the self-convolution of A073776.
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LINKS
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FORMULA
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G.f.: A(x)= x/(Sum_{n=1..infinity} mu(n)*x^n)^2, A(0)=1, where mu(n)=Moebius function.
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EXAMPLE
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MATHEMATICA
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A068341[n_] := A068341[n] = Sum[MoebiusMu[k]*MoebiusMu[n + 1 - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[-A068341[k + 1]*a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Oct 10 2011 *)
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PROG
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(Haskell)
a073777 n = a073777_list !! (n-1)
a073777_list = 1 : f [1] where
f xs = y : f (y : xs) where y = sum $ zipWith (*) xs ms'
ms' = map negate $ tail a068341_list
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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