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Search: id:A143596
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| A143596 |
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A symmetrical triangle sequence of coefficients of a difference polynomial' p(x,n)=((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x). |
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+0
2
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| 1, 2, 2, 2, 3, 6, 10, 6, 3, 4, 12, 28, 32, 28, 12, 4, 5, 20, 60, 100, 126, 100, 60, 20, 5, 6, 30, 110, 240, 396, 452, 396, 240, 110, 30, 6, 7, 42, 182, 490, 1001, 1484, 1716, 1484, 1001, 490, 182, 42, 7, 8, 56, 280, 896, 2184, 3976, 5720, 6400, 5720, 3976, 2184, 896, 280
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:{1, 6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776}.
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FORMULA
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p(x,n)=((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x); t(n,m)=coefficients(t(n,m)).
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EXAMPLE
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{1},
{2, 2, 2},
{3, 6, 10, 6, 3},
{4, 12, 28, 32, 28, 12, 4},
{5, 20, 60, 100, 126, 100, 60, 20, 5},
{6, 30, 110, 240, 396, 452, 396, 240, 110, 30, 6},
{7, 42, 182, 490, 1001, 1484, 1716, 1484, 1001, 490, 182, 42, 7},
{8, 56, 280, 896, 2184, 3976, 5720, 6400, 5720, 3976, 2184, 896, 280, 56, 8},
{9, 72, 408, 1512, 4284, 9240, 15912, 21816, 24310, 21816, 15912, 9240, 4284, 1512, 408, 72, 9},
{10, 90, 570, 2400, 7752, 19320, 38760, 62880, 83980, 92252, 83980, 62880, 38760, 19320, 7752, 2400, 570, 90, 10}
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MATHEMATICA
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Clear[p, x, n, m]; p[x_, n_] = ((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x); Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A057040 A096235 A147851 this_sequence A091712 A125721 A049798
Adjacent sequences: A143593 A143594 A143595 this_sequence A143597 A143598 A143599
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KEYWORD
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nonn,tabf
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 25 2008
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