OFFSET
1,5
COMMENTS
Row sums are 1.
FORMULA
Q(y,0)=1; Q(y,1)=y; Q(y, n) = -(-2 + 2*(1 - y) - 2*(1 - y)*Q(y, n - 1) + Q(y, n - 2)).
EXAMPLE
{1},
{0, 1},
{-1, 4, -2},
{-2, 11, -12, 4},
{-3, 24, -44, 32, -8},
{-4, 45, -124, 148, -80, 16},
{-5, 76, -294, 512, -448,192, -32},
{-6, 119, -616, 1464, -1840, 1264, -448,64},
{-7, 176, -1176, 3648, -6160, 6016, -3392, 1024, -128},
{-8, 249, -2088, 8184, -17776, 23088, -18368, 8768, -2304, 256},
{-9, 340, -3498, 16896, -45760, 75712, -79520, 53248, -22016, 5120, -512}
MATHEMATICA
P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - P[x, n - 2]; Solve[c*x0 + d - 2*x*(c*x1 + d) + c*x2 + d == 0, x0] c = -1; d = 1; (* Transform : c*x + d -> y*) Q[y, -1] = 0; Q[y, 0] = 1; Q[y, 1] = y; Q[y_, n_] := Q[y, n] = -(-2 + 2 (1 - y) - 2 (1 - y) Q[y, n - 1] + Q[y, n - 2]); Table[ExpandAll[Q[y, n]], {n, 0, 10}]; a = Table[CoefficientList[Q[y, n], y], {n, 0, 10}]; Flatten[a]
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Mar 16 2008
EXTENSIONS
Edited by Joerg Arndt, Nov 15 2014
STATUS
approved