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Search: id:A144394
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| A144394 |
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A triangle sequence of coefficients of a symmetrical polynomial: p(x,n)=((x + 1)^n - (x^n + n*x^(n - 1) + n*x + 1))/x^2. |
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+0
1
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| 6, 10, 10, 15, 20, 15, 21, 35, 35, 21, 28, 56, 70, 56, 28, 36, 84, 126, 126, 84, 36, 45, 120, 210, 252, 210, 120, 45, 55, 165, 330, 462, 462, 330, 165, 55, 66, 220, 495, 792, 924, 792, 495, 220, 66, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 91, 364, 1001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:{6, 20, 50, 112, 238, 492, 1002, 2024, 4070, 8164, 16354, 32736}.
Polynomial designed to isolate the interior of Pascals triangle;
it strips out the {1,n,...,n,1} four externals of the triangle sequence.
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FORMULA
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p(x,n)=((x + 1)^n - (x^n + n*x^(n - 1) + n*x + 1))/x^2; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{6},
{10, 10},
{15, 20, 15},
{21, 35, 35, 21},
{28, 56, 70, 56, 28},
{36, 84, 126, 126, 84, 36},
{45, 120, 210, 252, 210, 120, 45},
{55, 165, 330, 462, 462, 330, 165, 55},
{66, 220, 495, 792, 924, 792, 495, 220, 66},
{78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78},
{91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91},
{105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105}
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MATHEMATICA
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Clear[p, x, n]; p[x_, n_] = ((x + 1)^n - (x^n + n*x^(n - 1) + n*x + 1))/x^2; Table[ExpandAll[p[x, n]], {n, 4, 15}]; Table[CoefficientList[p[x, n], x], {n, 4, 15}]; Flatten[%]
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CROSSREFS
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Sequence in context: A127019 A024746 A111093 this_sequence A087873 A107014 A132628
Adjacent sequences: A144391 A144392 A144393 this_sequence A144395 A144396 A144397
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 02 2008
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