|
| |
|
|
A156647
|
|
A q factorial based on Shabat ChebyshevT (*A123583*) Polynomials as anti-diagonals: t(n,k)=If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {k, 1, n}]].
|
|
0
| |
|
|
1, 1, 1, 1, -3, 2, 1, -8, 144, 6, 1, -15, 2304, -97200, 24, 1, -24, 14400, -22579200, 914457600, 120, 1, -35, 57600, -857304000, 7517247897600, -119833267276800, 720, 1, -48, 176400, -13548902400, 3163657512960000, -85018329720343756800
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Row sums are:
{1, 2, 0, 143, -94886, 891892897, -112316876624914, 133704513357235842193,
27103010769819649354022285842, -424333626522806878030724503631699177935,
188993615959446996375698529818265962079281621759902,...}.
|
|
|
FORMULA
| t(n,k)=If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {k, 1, n}]];
out_(n,m)=anti-diagonal(t(n,m)).
|
|
|
EXAMPLE
| {1},
{1, 1},
{1, -3, 2},
{1, -8, 144, 6},
{1, -15, 2304, -97200, 24},
{1, -24, 14400, -22579200, 914457600, 120},
{1, -35, 57600, -857304000, 7517247897600, -119833267276800, 720},
{1, -48, 176400, -13548902400, 3163657512960000, -85018329720343756800, 218719679433615360000, 5040},
{1, -63, 451584, -126252126000, 312296780759040000, -723640387598472960000000, 32663974263892295087554560000, -5560239853997343915079680000, 40320},
{1, -80, 1016064, -824231116800, 12830569258066560000, -705361511315077913640960000, 10259703251199168078941798400000000, -426312653106013289987130264523898880000, 1968766880660574286811328573603840000, 362880},
{1, -99, 2073600, -4162382380800, 291843331830212198400, -185148397415809368581040000000, 156112204929847034027226757595136000000, -9016240073947062599243543038650537984000000000, 189012341549418940577867716643736686438897418240000, \-9709350054109344314641919335334538313728000000, 3628800}
|
|
|
MATHEMATICA
| Clear[t, n, m, i, k, a, b];
t[n_, m_] = If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {k, 1, n}]];
a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];
b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];
Flatten[%]
|
|
|
CROSSREFS
| Sequence in context: A101908 A086963 A079749 * A183154 A193791 A160760
Adjacent sequences: A156644 A156645 A156646 * A156648 A156649 A156650
|
|
|
KEYWORD
| sign,tabl,uned
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 12 2009
|
| |
|
|
