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Search: id:A157077
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| A157077 |
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A triangle of Legengdre P polynomial coefficients: p(x,n)=2^n*LegendreP[n, x]. |
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1
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| 1, 0, 2, -2, 0, 6, 0, -12, 0, 20, 6, 0, -60, 0, 70, 0, 60, 0, -280, 0, 252, -20, 0, 420, 0, -1260, 0, 924, 0, -280, 0, 2520, 0, -5544, 0, 3432, 70, 0, -2520, 0, 13860, 0, -24024, 0, 12870, 0, 1260, 0, -18480, 0, 72072, 0, -102960, 0, 48620, -252, 0, 13860, 0, -120120
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are:2^n
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...}.
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FORMULA
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p(x,n)=2^n*LegendreP[n, x];
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{1},
{0, 2},
{-2, 0, 6},
{0, -12, 0, 20},
{6, 0, -60, 0, 70},
{0, 60, 0, -280, 0, 252},
{-20, 0, 420, 0, -1260, 0, 924},
{0, -280, 0, 2520, 0, -5544, 0, 3432},
{70, 0, -2520, 0, 13860, 0, -24024, 0, 12870},
{0, 1260, 0, -18480, 0, 72072, 0, -102960, 0, 48620},
{-252, 0, 13860, 0, -120120, 0, 360360, 0, -437580, 0, 184756}
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MATHEMATICA
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Table[CoefficientList[2^n*LegendreP[n, x], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A088972 A100334 A129936 this_sequence A076256 A127467 A140333
Adjacent sequences: A157074 A157075 A157076 this_sequence A157078 A157079 A157080
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KEYWORD
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tabl,uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 22 2009
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