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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
OFFSET
1,7
COMMENTS
Row sums are 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
LINKS
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
KEYWORD
uned,tabl,sign
AUTHOR
Roger L. Bagula, Mar 31 2008
STATUS
approved