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A144393
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A triangle sequence of coefficients of a symmetrical polynomial: p(x,n)=x^n + n*x^(n - 1) + n*x + 1.
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0
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2, 2, 2, 1, 4, 1, 1, 3, 3, 1, 1, 4, 0, 4, 1, 1, 5, 0, 0, 5, 1, 1, 6, 0, 0, 0, 6, 1, 1, 7, 0, 0, 0, 0, 7, 1, 1, 8, 0, 0, 0, 0, 0, 8, 1, 1, 9, 0, 0, 0, 0, 0, 0, 9, 1, 1, 10, 0, 0, 0, 0, 0, 0, 0, 10, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}.
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FORMULA
| p(x,n)=x^n + n*x^(n - 1) + n*x + 1; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {2},
{2, 2},
{1, 4, 1},
{1, 3, 3, 1},
{1, 4, 0, 4, 1},
{1, 5, 0, 0, 5, 1},
{1, 6, 0, 0, 0, 6, 1},
{1, 7, 0, 0, 0, 0, 7, 1},
{1, 8, 0, 0, 0, 0, 0, 8, 1},
{1, 9, 0, 0, 0, 0, 0, 0, 9, 1},
{1, 10, 0, 0, 0, 0, 0, 0, 0, 10, 1}
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MATHEMATICA
| Clear[p, x, n]; p[x_, n_] = x^n + n*x^(n - 1) + n*x + 1; Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A089258 A004065 A127496 * A089400 A180824 A105777
Adjacent sequences: A144390 A144391 A144392 * A144394 A144395 A144396
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 02 2008
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