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A159041
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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).
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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, -8, -48, 136, 1908, -3968, -121040, 176896, 11561820, -11184128,...}.
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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)
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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}
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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[%]
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CROSSREFS
| A008292
Sequence in context: A202941 A166341 A113280 * A154979 A146765 A190152
Adjacent sequences: A159038 A159039 A159040 * A159042 A159043 A159044
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 03 2009
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