|
Search: id:A159041
|
|
|
| A159041 |
|
A triangle of polynomial coefficients: p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal) Floor[n/2], (-1)^i*A008292[n+1, i+1], -(-1)^(n - i)* A008292[n+1, i+1]]], {i, 0, n}]/(1 - x). |
|
+0
1
|
|
| 1, 1, 1, 1, -10, 1, 1, -25, -25, 1, 1, -56, 246, -56, 1, 1, -119, 1072, 1072, -119, 1, 1, -246, 4047, -11572, 4047, -246, 1, 1, -501, 14107, -74127, -74127, 14107, -501, 1, 1, -1012, 46828, -408364, 901990, -408364, 46828, -1012, 1, 1, -2035, 150602
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:
{1, 2, -8, -48, 136, 1908, -3968, -121040, 176896, 11561820, -11184128,...}.
|
|
FORMULA
|
p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal) Floor[n/2], (-1)^i*A008292[n+1, i+1], -(-1)^(n - i)* A008292[n+1, i+1]]], {i, 0, n}]/(1 - x);
t(n,m)=coefficients(p(x,n),x)
|
|
EXAMPLE
|
{1},
{1, 1},
{1, -10, 1},
{1, -25, -25, 1},
{1, -56, 246, -56, 1},
{1, -119, 1072, 1072, -119, 1},
{1, -246, 4047, -11572, 4047, -246, 1},
{1, -501, 14107, -74127, -74127, 14107, -501, 1},
{1, -1012, 46828, -408364, 901990, -408364, 46828, -1012, 1},
{1, -2035, 150602, -2052886, 7685228, 7685228, -2052886, 150602, -2035, 1},
{ 1, -4082, 474189, -9713496, 56604978, -105907308, 56604978, -9713496, 474189, -4082, 1}
|
|
MATHEMATICA
|
Clear[A, p, n, i];
A[n_, 1] := 1;
A[n_, n_] := 1;
A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k];
p[x_, n_] = Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], (-1)^i*A[n, i], -(-1)^(n - i)*A[n, i]]], {i, 0, n}]/(1 - x);
Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}];
Flatten[%]
|
|
CROSSREFS
|
A008292
Sequence in context: A146773 A166341 A113280 this_sequence A154979 A146765 A154984
Adjacent sequences: A159038 A159039 A159040 this_sequence A159042 A159043 A159044
|
|
KEYWORD
|
sign,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 03 2009
|
|
|
Search completed in 0.002 seconds
|
