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A144394
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Triangle: coefficients of the symmetrical polynomial p(x,n)=((x + 1)^n - (x^n + n*x^(n - 1) + n*x + 1))/x^2.
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0
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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; table; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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COMMENTS
| Interior of Pascal's triangle, stripping out the initial 1,n and final n,1 in each row.
The first term in the sequence is T(4,0); each row has 0 <= k <= n-4.
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FORMULA
| T(n,k) = C(n,k+2).
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EXAMPLE
| {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
| 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
| Cf. A007318, A052515 (row sums), A024746 (sorted).
Sequence in context: A175612 A024746 A111093 * A087873 A107014 A206036
Adjacent sequences: A144391 A144392 A144393 * A144395 A144396 A144397
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 02 2008
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EXTENSIONS
| Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2010
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