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A346838
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a(n) = (PolyLog(-n, -i) - exp(i*Pi*n)*PolyLog(-n, i)) * i / exp(i*Pi*n/2).
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3
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1, -1, 1, -2, 5, -16, 61, -272, 1385, -7936, 50521, -353792, 2702765, -22368256, 199360981, -1903757312, 19391512145, -209865342976, 2404879675441, -29088885112832, 370371188237525, -4951498053124096, 69348874393137901, -1015423886506852352, 15514534163557086905
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OFFSET
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0,4
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COMMENTS
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This is a signed variant of A000111. The author named the interpolating function of A000111 the 'André function' and the interpolating function of this sequence the 'signed André function'. See the illustrating file in the links section for the definitions.
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LINKS
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FORMULA
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log(abs(a(n))) = log(A000111(n)) ~ log(4) + (1/2 + n)*log(2*n/Pi) + ((2/7) - n^2 + 30*n^4 - 360*n^6) / (360*n^5).
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MAPLE
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b:= proc(u, o) option remember; `if`(u+o=0, 1,
add(b(o+j-1, u-j), j=1..u))
end:
a:= n-> (-1)^n*b(n, 0):
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MATHEMATICA
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a[n_] := I (PolyLog[-n, -I] - Exp[I Pi n] PolyLog[-n, I]) / Exp[I Pi n / 2];
Table[a[n], {n, 0, 24}]
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PROG
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(Julia)
using Nemo
CC = ComplexField(80); I = onei(CC); Pi = const_pi(CC)
A(n) = I*(polylog(-n, -I) - exp(I*Pi*n)*polylog(-n, I)) / exp(I*Pi*n/CC(2))
[unique_integer(A(CC(n)))[2] for n in 0:24] |> println
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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