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A178120
Coefficient array of orthogonal polynomials P(n,x)=(x-2n)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1,P(1,x)=x-2.
3
1, -2, 1, 7, -6, 1, -36, 40, -12, 1, 253, -326, 131, -20, 1, -2278, 3233, -1552, 324, -30, 1, 25059, -38140, 20678, -5260, 675, -42, 1, -325768, 523456, -310560, 90754, -14380, 1252, -56, 1, 4886521, -8205244, 5223602, -1694244, 312059, -33866, 2135, -72, 1
OFFSET
0,2
COMMENTS
Inverse is A178121. First column is A112293 signed.
EXAMPLE
Triangle begins
1,
-2, 1,
7, -6, 1,
-36, 40, -12, 1,
253, -326, 131, -20, 1,
-2278, 3233, -1552, 324, -30, 1,
25059, -38140, 20678, -5260, 675, -42, 1,
-325768, 523456, -310560, 90754, -14380, 1252, -56, 1,
4886521, -8205244, 5223602, -1694244, 312059, -33866, 2135, -72, 1
Production matrix of inverse is
2, 1,
1, 4, 1,
0, 3, 6, 1,
0, 0, 5, 8, 1,
0, 0, 0, 7, 10, 1,
0, 0, 0, 0, 9, 12, 1,
0, 0, 0, 0, 0, 11, 14, 1,
0, 0, 0, 0, 0, 0, 13, 16, 1,
0, 0, 0, 0, 0, 0, 0, 15, 18, 1
MAPLE
A178120 := proc(n, k)
if n = k then
1;
elif n = 1 and k = 0 then
-2 ;
elif k < 0 or k > n then
0 ;
else
-2*n*procname(n-1, k)+procname(n-1, k-1)-(2*n-3)*procname(n-2, k) ;
end if;
end proc: # R. J. Mathar, Dec 03 2014
MATHEMATICA
P[0, _] = 1;
P[1, x_] := x - 2;
P[n_, x_] := P[n, x] = (x-2n) P[n-1, x] - (2n-3) P[n-2, x];
T[n_] := Module[{x}, CoefficientList[P[n, x], x]];
Table[T[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, Aug 06 2023 *)
CROSSREFS
Sequence in context: A157743 A135895 A039814 * A180568 A373050 A248950
KEYWORD
sign,easy,tabl
AUTHOR
Paul Barry, May 20 2010
STATUS
approved