A139809 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_{m=0..n} Sum_{i=0..m} (d/dx) T(x,i+1).

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

Offset

1,3

Comments

Row sums: {1, 5, 70, 2100, 115500, 10510500, 1471470000, 300179880000, 85551265800000, 32937237333000000, 16666242090498000000}.

Triangle sequence is of the Mahonian number general type: A008302.

Links

Table of n, a(n) for n=1..43.

Formula

Coefficients of p(x,n) = Product_{m=0..n} Sum_{i=0..m} (d/dx) T(x,i+1).

Example

{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}

Mathematica

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]

Crossrefs

Cf. A008302.

Sequence in context: A261254 A168613 A248251 * A348640 A094099 A107046

Adjacent sequences: A139806 A139807 A139808 * A139810 A139811 A139812

Keyword

uned,tabf,sign

Author

Roger L. Bagula, Jun 14 2008

Status

approved