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A097632
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a(n) = 2^n * Lucas(n) * (n-1)!.
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1
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2, 12, 64, 672, 8448, 138240, 2672640, 60641280, 1568931840, 45705461760, 1478924697600, 52646746521600, 2044394156851200, 86005817907609600, 3896481847600742400, 189139342470414336000, 9793081532749971456000, 538748376721309827072000, 31381673358053118836736000
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OFFSET
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1,1
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COMMENTS
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Number of possible well-colored cycles on n nodes. Well-colored means, each green vertex has at least a red child, each red vertex has no red child.
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LINKS
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FORMULA
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E.g.f.: -log(1-2*x-4*x^2).
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MATHEMATICA
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a[n_] := 2^n*LucasL[n, 1]*(n-1)!; Array[a, 19] (* or *)
nmax=19; CoefficientList[Series[-Log[1-2x-4x^2], {x, 0, nmax}], x]Range[0, nmax]! (* Stefano Spezia, Jan 15 2024 *)
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PROG
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(Python)
L0, L1, F, i = 1, 2, 2, 1
while i < n:
L0, L1, F, i = L0+L1, L0, 2*i*F, i+1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition corrected by and a(18)-a(19) from Stefano Spezia, Jan 15 2024
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STATUS
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approved
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