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Search: id:A139809
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| A139809 |
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A triangle of coefficients of a product polynomial sequence based on Chebyshev T:differentiation of T[(x,n) which gives U(x,n): p(x,n)=Product[Sum[d/dx(T(x,i+1)),{i,0,m}]{m,0,n}]. |
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+0
1
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| 1, 1, 4, -2, -4, 28, 48, 4, 32, -32, -544, -368, 1472, 1536, 12, 48, -672, -2656, 8304, 36480, -15360, -144384, -56064, 166912, 122880, 36, 432, -1440, -28320, -13296, 549888, 811264, -4222976, -8578560, 13056000, 35942400, -10592256, -64811008, -17072128, 41877504, 23592960, -144, -864
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 5, 70, 2100, 115500, 10510500, 1471470000, 300179880000, 85551265800000, 32937237333000000, 16666242090498000000}
Triangle sequence if of the Mahonian number general type: A008302
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FORMULA
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p(x,n)=Product[Sum[d/dx(T(x,i+1)),{i,0,m}]{m,0,n}]; Out_n,m=Coefficients(P(x,n))
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EXAMPLE
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{1},
{1, 4},
{-2, -4, 28, 48},
{4,32, -32, -544, -368, 1472, 1536},
{12, 48, -672, -2656, 8304, 36480, -15360, -144384, -56064, 166912, 122880}, {36, 432, -1440, -28320, -13296, 549888, 811264, -4222976, -8578560, 13056000,35942400, -10592256, -64811008, -17072128, 41877504, 23592960},
{-144, -864, 20448, 124800, -885696, -5887104, 13678208, 117986816, -57368064,
-1173855232, -473961472, 6273417216, 5899501568, -18314887168, -25248595968,
27066105856, 53500837888, -12863668224, -56189255680, -10932453376,23290970112, 10569646080}
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MATHEMATICA
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p[x_, n_] = Product[Sum[D[ChebyshevT[i + 1, x], x], {i, 0, m}], {m, 0, n}] Table[ExpandAll[p[x, n]], {n, 0, 10}] a = Table[CoefficientList[p[x, n], x], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Cf. A008302.
Sequence in context: A011302 A085689 A134434 this_sequence A094099 A107046 A072907
Adjacent sequences: A139806 A139807 A139808 this_sequence A139810 A139811 A139812
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KEYWORD
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uned,tabf,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 14 2008
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