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A136620 Triangle of coefficients from polynomial recursion P(x,n)=(1-x)*P(x,n-1) - binomial(x-1,2)*P(x,n-2). 0
1, 1, -1, 0, -1, 1, -2, 4, -2, -4, 14, -17, 8, -1, 0, 4, -13, 15, -7, 1, 8, -32, 46, -25, -1, 5, -1, 8, -48, 116, -144, 96, -32, 4, 0, -24, 132, -300, 361, -244, 90, -16, 1, -16, 96, -228, 252, -79, -109, 134, -62, 13, -1, -32, 272, -984, 1980, -2416, 1811, -787, 154, 10, -9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row sums are 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

LINKS

Table of n, a(n) for n=1..64.

Michael Gromov, Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits), Publications Math. de l'IHES, 53 (1981), p. 53-78; see p. 75

FORMULA

P[x, -1] = 0; P[x, 0] = 1; P[x, 1] = 1 - x; P(x,n)=(1-x)*P(x,n-1)-binomial[x-1,2]*P(x,n-2) Output as 2^Floor[n/2]*P(x,n) to get Integers.

EXAMPLE

1;

1, -1;

0, -1, 1;

-2, 4, -2;

-4, 14, -17,8, -1;

0, 4, -13, 15, -7, 1;

8, -32, 46, -25, -1, 5, -1;

8, -48, 116, -144, 96, -32, 4;

0, -24, 132, -300, 361, -244,90, -16, 1;

-16, 96, -228, 252, -79, -109, 134, -62, 13, -1;

-32, 272, -984, 1980, -2416, 1811, -787, 154, 10, -9, 1;

MATHEMATICA

P[x, -1] = 0; P[x, 0] = 1; P[x, 1] = 1 - x; P[x_, n_] := P[x, n] = (1 - x)*P[x, n - 1] - Binomial[x - 1, 2]*P[x, n - 2];

Table[ExpandAll[2^Floor[n/2]*P[x, n]], {n, 0, 10}];

a = Table[CoefficientList[2^Floor[n/2]*P[x, n], x], {n, 0, 10}]; Flatten[a]

CROSSREFS

Sequence in context: A055372 A241078 A198285 * A139548 A193378 A108445

Adjacent sequences:  A136617 A136618 A136619 * A136621 A136622 A136623

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Mar 31 2008

STATUS

approved

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Last modified August 17 22:43 EDT 2022. Contains 356195 sequences. (Running on oeis4.)