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A146568
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Coefficients of Pascals triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x.
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0
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4, 20, 20, 72, 224, 72, 232, 1672, 1672, 232, 716, 10528, 23528, 10528, 716, 2172, 60636, 259688, 259688, 60636, 2172, 6544, 331584, 2485232, 4674944, 2485232, 331584, 6544, 19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Row sums starting with n=2 are:{4, 40, 368, 3808, 46016, 644992, 10321664, 185794048, 3715890176}. First elements in each row are:f[n_] = 3^n - 2*n - 1;A061981.
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FORMULA
| q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 2.
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EXAMPLE
| {4}, {20, 20}, {72, 224, 72}, {232, 1672, 1672, 232}, {716, 10528, 23528, 10528, 716}, {2172, 60636, 259688, 259688, 60636, 2172}, {6544, 331584, 2485232, 4674944, 2485232, 331584, 6544}, {19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 19664}, {59028, 9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096, 59028}
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MATHEMATICA
| q[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p[x_, n_] = (q[x, n] - (x + 1)^n)/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 2, 10}]; Flatten[%]
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CROSSREFS
| A061981, A060187
Sequence in context: A130316 A131745 A151727 * A087326 A065984 A039569
Adjacent sequences: A146565 A146566 A146567 * A146569 A146570 A146571
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2008
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