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Search: id:A146773
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| A146773 |
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A new symmetrical polynomial form to give a triangle sequence: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. |
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1
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| 1, 1, 1, 1, 10, 1, 1, 19, 19, 1, 1, 52, 38, 52, 1, 1, 133, 106, 106, 133, 1, 1, 326, 399, 148, 399, 326, 1, 1, 775, 1301, 547, 547, 1301, 775, 1, 1, 1800, 3868, 2616, 582, 2616, 3868, 1800, 1, 1, 4105, 10788, 10324, 2686, 2686, 10324, 10788, 4105, 1, 1, 9226, 28717
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:{1, 2, 12, 40, 144, 480, 1600, 5248, 17152, 55808, 181248}.
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FORMULA
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p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{1}, {1, 1}, {1, 10, 1}, {1, 19, 19, 1}, {1, 52, 38, 52, 1}, {1, 133, 106, 106, 133, 1}, {1, 326, 399, 148, 399, 326, 1}, {1, 775, 1301, 547, 547, 1301, 775, 1}, {1, 1800, 3868, 2616, 582, 2616, 3868, 1800, 1}, {1, 4105, 10788, 10324, 2686, 2686, 10324, 10788, 4105, 1}, {1, 9226, 28717, 35960, 15570, 2300, 15570, 35960, 28717, 9226, 1}
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MATHEMATICA
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Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A096089 A010176 A143683 this_sequence A166341 A113280 A159041
Adjacent sequences: A146770 A146771 A146772 this_sequence A146774 A146775 A146776
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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 02 2008
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