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A143196
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Triangle read by rows: real part of Lerch Phi expansion of A060187: p(x,n)=2^n*(1 - I*x)*(1 + n)* LerchPhi[I*x, -n, 1/2].
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0
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1, 1, 0, 1, 0, -1, 1, 0, -23, 0, 1, 0, -230, 0, 1, 1, 0, -1682, 0, 237, 0, 1, 0, -10543, 0, 10543, 0, -1, 1, 0, -60657, 0, 259723, 0, -2179, 0, 1, 0, -331612, 0, 4675014, 0, -331612, 0, 1, 1, 0, -1756340, 0, 69413294, 0, -21707972, 0, 19673, 0, 1, 0, -9116141, 0, 906923282, 0, -906923282, 0, 9116141, 0, -1
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OFFSET
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1,9
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COMMENTS
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Row sums are: {1, 1, 0, -22, -228, -1444, 0, 196888, 4011792, 45968656, 0, ...}.
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LINKS
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Table of n, a(n) for n=1..66.
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FORMULA
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p(x,n)=2^n*(1 - I*x)*(1 + n)* LerchPhi[I*x, -n, 1/2]; t(n,m)=RealCoefficients(p(x,n)).
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EXAMPLE
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{1},
{1, 0},
{1, 0, -1},
{1, 0, -23, 0},
{1, 0, -230, 0, 1},
{1, 0, -1682, 0, 237, 0},
{1, 0, -10543, 0, 10543, 0, -1},
{1, 0, -60657,0, 259723, 0, -2179, 0},
{1, 0, -331612, 0, 4675014, 0, -331612, 0, 1},
{1, 0, -1756340, 0, 69413294, 0, -21707972, 0, 19673, 0},
{1, 0, -9116141, 0, 906923282, 0, -906923282, 0, 9116141, 0, -1}
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MATHEMATICA
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Clear[p, x, n, a]; p[x_, n_] = p[x_, n_] = 2^n*(1 - I*x)*(1 + n)* LerchPhi[I*x, -n, 1/2]; Table[FullSimplify[Expand[p[x, n]]], {n, 0, 10}]; Table[Re[CoefficientList[FullSimplify[Expand[p[x, n]]], x]], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Cf. A060187.
Sequence in context: A180729 A119566 * A143197 A092993 A114784 A141517
Adjacent sequences: A143193 A143194 A143195 * A143197 A143198 A143199
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KEYWORD
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tabl,sign
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AUTHOR
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Roger L. Bagula, Oct 19 2008
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EXTENSIONS
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What are the imaginary parts? - N. J. A. Sloane, Oct 25 2008
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STATUS
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approved
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