A139808 A triangle of coefficients of a product polynomial sequence based on Chebyshev T[(x,n): p(x,n) = Product_{m=0..n} Sum_{i=0..m} T(x,i).

1, 1, 1, 0, 1, 3, 2, 0, 0, -2, -4, 6, 16, 8, 0, 0, -2, 0, 26, 20, -92, -120, 64, 160, 64, 0, 0, -2, -6, 38, 130, -204, -964, 144, 3120, 1664, -4224, -4352, 1280, 3072, 1024, 0, 0, 0, -6, -42, 74, 1022, 548, -9100, -12656, 37968, 79584, -70336, -243712, 7168, 389632, 179200, -292864, -258048, 49152, 114688

Offset

1,6

Comments

Row sums are (n+1)!.

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

Links

Table of n, a(n) for n=1..62.

Formula

Coefficients of Product_{m=0..n} Sum_{i=0..m} T(x,i).

Example

{1},
{1, 1},
{0, 1, 3, 2},
{0, 0, -2, -4, 6, 16, 8},
{0, 0, -2, 0,26, 20, -92, -120, 64, 160, 64},
{0, 0, -2, -6, 38,130, -204, -964, 144, 3120, 1664, -4224, -4352, 1280, 3072, 1024},
{0, 0, 0, -6, -42, 74, 1022,548, -9100, -12656, 37968, 79584, -70336, -243712, 7168, 389632, 179200, -292864, -258048, 49152, 114688,32768},
{0, 0, 0, 0, 24, 96, -1040, -4640, 15288, 84736, -86368, -788096, -20128, 4217856, 2754304, -13582336, -15642624, 25722880,44859392, -23887872, -74948608, -2752512, 72318976, 29884416, -34996224, -27262976, 3670016, 8388608, 2097152}

Mathematica

p[x_, n_] = Product[Sum[ChebyshevT[i, 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: A214851 A245203 A133949 * A055654 A170849 A292260

Adjacent sequences: A139805 A139806 A139807 * A139809 A139810 A139811

Keyword

uned,tabf,sign

Author

Roger L. Bagula, Jun 14 2008

Status

approved