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Search: id:A146745
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| A146745 |
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Coefficients of Pascals triangle polynomial minus MacMahon polynomial A060187 with minus the first and last row terms and powers of x divided out: f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x. |
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| 224, 1672, 1672, 10528, 23528, 10528, 60636, 259688, 259688, 60636, 331584, 2485232, 4674944, 2485232, 331584, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 9116096, 178300784, 906923072, 1527092216, 906923072
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Row sums starting with n=4 are:{224, 3344, 44584, 640648, 10308576, 185754720, 3715772120}. First elements in each row are:{224, 1672, 1672, 10528, 60636, 331584, 1756304, 9116096}. Subtracting out the row terms gives the middle elements of the difference.
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FORMULA
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f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 4.
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EXAMPLE
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{224}, {1672, 1672}, {10528, 23528, 10528}, {60636, 259688, 259688, 60636}, {331584, 2485232, 4674944, 2485232, 331584}, {1756304, 21707888, 69413168, 69413168, 21707888, 1756304}, {9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096}
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MATHEMATICA
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q[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p[x_, n_] = ((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 4, 10}]; Flatten[%]
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CROSSREFS
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A061981, A060187
Sequence in context: A158227 A061524 A156813 this_sequence A015048 A032802 A007771
Adjacent sequences: A146742 A146743 A146744 this_sequence A146746 A146747 A146748
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2008
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