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.

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.

Links

Table of n, a(n) for n=0..44.

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 A248950 A329058

Adjacent sequences: A178117 A178118 A178119 * A178121 A178122 A178123

Keyword

sign,easy,tabl

Author

Paul Barry, May 20 2010

Status

approved