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A136202 Triangle read by rows: expansion of Q(y, n), where 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)). 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are 1.

LINKS

Table of n, a(n) for n=1..60.

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

Cf. A053120.

Sequence in context: A095800 A055630 A182700 * A075418 A199221 A096870

Adjacent sequences:  A136199 A136200 A136201 * A136203 A136204 A136205

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Mar 16 2008

EXTENSIONS

Edited by Joerg Arndt, Nov 15 2014

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)