OFFSET
0,7
LINKS
Robert Israel, Table of n, a(n) for n = 0..945 (rows 0 to 42, flattened)
FORMULA
a(n, k) = Sum_{i=0..n} a(n, i)*k^i, 0<=k<=n.
EXAMPLE
1;
x;
x^2-x-1;
10*x^3-29*x^2-6*x+19;
57*x^4-325*x^3+287*x^2+423*x-19;
12813*x^5-120862*x^4+291323*x^3+44088*x^2-355855*x-227362.
MAPLE
f:= proc(n) uses LinearAlgebra:
local V, d, i;
V:= op(NullSpace(VandermondeMatrix([$0..n])-IdentityMatrix(n+1)));
if V[-1] < 0 then V:= -V fi;
d:= ilcm(seq(denom(V[i]), i=1..n+1));
seq(d*V[-i], i=1..n+1)
end proc:
seq(f(i), i=0..10); # Robert Israel, Jan 03 2016
MATHEMATICA
VM[n_] := Table[If[k == 1, 1, (j-1)^(k-1)], {j, 1, n}, {k, 1, n}];
f[n_] := Module[{V, d}, V = NullSpace[VM[n+1] - IdentityMatrix[n+1]][[1]]; If[V[[-1]] < 0, V = -V]; d = LCM @@ Denominator[V]; d V // Reverse];
f /@ Range[0, 10] // Flatten (* Jean-François Alcover, Jun 16 2020, after Robert Israel *)
PROG
(PARI) { f(n) = local(v); v=matkerint(matrix(n+1, n+1, i, j, (i-1)^(j-1)-(i==j))); c=vector(n+1, i, v[n+2-i, 1]); if(c[1]<0, for(i=1, n+1, c[i]=-c[i])); return(c); } \\ function f(n) generate coefficients of the polynomial of degree n (Alekseyev)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Feb 05 2005
EXTENSIONS
More terms from Max Alekseyev, Feb 09 2005
STATUS
approved