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A147565
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Average of Pascal's triangle and MacMahon numbers: p(x,n)=((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2.
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0
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1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 40, 118, 40, 1, 1, 121, 846, 846, 121, 1, 1, 364, 5279, 11784, 5279, 364, 1, 1, 1093, 30339, 129879, 129879, 30339, 1093, 1, 1, 3280, 165820, 1242672, 2337542, 1242672, 165820, 3280, 1, 1, 9841, 878188, 10854028, 34706710
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are: {1, 2, 6, 28, 200, 1936, 23072, 322624, 5161088, 92897536, 1857946112,...}.
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FORMULA
| p(x,n)=((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1}, {1, 1}, {1, 4, 1}, {1, 13, 13, 1}, {1, 40, 118, 40, 1}, {1, 121, 846, 846, 121, 1}, {1, 364, 5279, 11784, 5279, 364, 1}, {1, 1093, 30339, 129879, 129879, 30339, 1093, 1}, {1, 3280, 165820, 1242672, 2337542, 1242672, 165820, 3280, 1}, {1, 9841, 878188, 10854028, 34706710, 34706710, 10854028, 878188, 9841, 1}, {1, 29524, 4558093, 89150512, 453461746, 763546360, 453461746, 89150512, 4558093, 29524, 1}
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MATHEMATICA
| Clear[t, p, x, n]; p[x_, n_] = ((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A146956 A152613 A157153 * A022167 A064281 A050154
Adjacent sequences: A147562 A147563 A147564 * A147566 A147567 A147568
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 07 2008
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