A135552 Riordan array (1/((1-2x)(1-x)^2), -x/(1-x)^2).

1, 4, -1, 11, -6, 1, 26, -22, 8, -1, 57, -64, 37, -10, 1, 120, -163, 130, -56, 12, -1, 247, -382, 386, -232, 79, -14, 1, 502, -848, 1024, -794, 378, -106, 16, -1, 1013, -1816, 2510, -2380, 1471, -576, 137, -18, 1, 2036, -3797, 5812, -6476, 4944, -2517, 834, -172, 20, -1, 4083, -7814, 12911, -16384, 14893, -9402, 4048, -1160, 211, -22, 1

Offset: 1

Author

Roger L. Bagula, Apr 08 2008

Keywords

• tabl
• sign

Comments

Row sums are A024495. First column is essentially A000295, second column is essentially -A002663. - Ralf Stephan, Jan 03 2014

Examples

			{1},
{4, -1},
{11, -6, 1},
{26, -22, 8, -1},
{57, -64, 37, -10, 1},
{120, -163, 130, -56, 12, -1},
{247, -382, 386, -232, 79, -14, 1},
{502, -848, 1024, -794, 378, -106, 16, -1},
{1013, -1816, 2510, -2380, 1471, -576, 137, -18, 1},
{2036, -3797, 5812, -6476, 4944, -2517, 834, -172, 20, -1},
{4083, -7814, 12911, -16384, 14893, -9402, 4048, -1160, 211, -22, 1}
		

Links

• G. C. Greubel, Table of n, a(n) for the first 25 rows

Crossrefs

Cf. A136674, A109954.

Programs

Mathematica

Clear[p, x, n, a]; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 4 - x; p[x_, n_] := p[x, n] = (4 - x)*p[x, n - 1] + (-5 + 2*x)*p[x, n - 2] + 2*p[x, n - 3]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

Formula

Coefficients of polynomials defined by recurrence: c0=2; p(x, n) = (2 + c0 - x)*p(x, n - 1) + (-1 - c0 (2 - x))*p(x, n - 2) + c0*p(x, n - 3).

Extensions

New name from Ralf Stephan, Jan 03 2014