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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 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.)