|
Search: id:A136457
|
|
|
| A136457 |
|
Triangle read by rows: coefficients of polynomials defined by recursion p(x,n)=(x-Gamma(n))*p(x,n-1). |
|
+0
1
|
|
| 1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 12, -32, 29, -10, 1, -288, 780, -728, 269, -34, 1, 34560, -93888, 88140, -33008, 4349, -154, 1, -24883200, 67633920, -63554688, 23853900, -3164288, 115229, -874, 1, 125411328000, -340899840000, 320383261440, -120287210688, 15971865420, -583918448, 4520189
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
These are inspired by Cornelius-Schultz matrices.
Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}
|
|
REFERENCES
|
E. F. Cornnelius and Phill Shultz, Amer. Math. Monthly, No. 2, 2008.
|
|
FORMULA
|
p(x,0)=1; p(x,1)=x-1; p(x,n)=(x-Gamma(n))*p(x,n-1)
|
|
EXAMPLE
|
Triangle begins:
{1},
{-1, 1},
{1, -2, 1},
{-2, 5, -4, 1},
{12, -32, 29, -10, 1},
{-288, 780, -728, 269, -34, 1},
{34560, -93888, 88140, -33008, 4349, -154, 1}
|
|
MATHEMATICA
|
Clear[p, x, n, a] p[x, 0] = 1; p[x, 1] = x - 1; p[x_, m_] := p[x, n] = (x - Gamma[n])*p[x, n - 1]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]; Table[ExpandAll[p[x, n]], {n, 0, 10}];
|
|
CROSSREFS
|
Adjacent sequences: A136454 A136455 A136456 this_sequence A136458 A136459 A136460
Sequence in context: A104560 A121435 A137156 this_sequence A078016 A078046 A084600
|
|
KEYWORD
|
tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
|
|
EXTENSIONS
|
Edited by njas, Aug 10 2008
|
|
|
Search completed in 0.002 seconds
|
