A182824 Inverse of coefficient array for orthogonal polynomials p(n,x)=(x-(2n-1))*p(n-1,x)-(2n-2)^2*p(n-2,x).

1, 1, 1, 5, 4, 1, 21, 33, 9, 1, 153, 264, 114, 16, 1, 1209, 2769, 1410, 290, 25, 1, 12285, 32076, 20259, 5040, 615, 36, 1, 140589, 432657, 314811, 94899, 14175, 1155, 49, 1, 1871217, 6475536, 5423076, 1886304, 337974, 33936, 1988, 64, 1, 27773361, 108067041, 101497860, 40257540, 8321670, 997542, 72324, 3204, 81, 1, 460041525, 1975940244, 2064827781, 915887520, 214906770, 29709288, 2565738, 141120, 4905, 100, 1

Offset

0,4

Comments

Inverse is the coefficient array for the orthogonal polynomials p(0,x)=1,p(1,x)=x-1,p(n,x)=(x-(2n-1))*p(n-1,x)-(2n-2)^2*p(n-2,x).

Inverse is A182826. First column is A182825.

Links

Table of n, a(n) for n=0..65.

Formula

Exponential Riordan array [1/(cos(sqrt(3)*x)-sin(sqrt(3)*x)/sqrt(3)), sin(sqrt(3)*x)/(sqrt(3)*cos(sqrt(3)*x)-sin(sqrt(3)*x))].

Example

Triangle begins
1,
1, 1,
5, 4, 1,
21, 33, 9, 1,
153, 264, 114, 16, 1,
1209, 2769, 1410, 290, 25, 1,
12285, 32076, 20259, 5040, 615, 36, 1,
140589, 432657, 314811, 94899, 14175, 1155, 49, 1,
1871217, 6475536, 5423076, 1886304, 337974, 33936, 1988, 64, 1
Production matrix begins
1, 1,
4, 3, 1,
0, 16, 5, 1,
0, 0, 36, 7, 1,
0, 0, 0, 64, 9, 1,
0, 0, 0, 0, 100, 11, 1,
0, 0, 0, 0, 0, 144, 13, 1,
0, 0, 0, 0, 0, 0, 196, 15, 1,
0, 0, 0, 0, 0, 0, 0, 256, 17, 1
0, 0, 0, 0, 0, 0, 0, 0, 324, 19, 1

Mathematica

* The function RiordanArray is defined in A256893. *)
RiordanArray[1/(Cos[Sqrt[3]*#] - Sin[Sqrt[3]*#]/Sqrt[3])&, Sin[Sqrt[3]*#]/ (Sqrt[3]*Cos[Sqrt[3]*#] - Sin[Sqrt[3]*#])&, 11, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

Crossrefs

Sequence in context: A365465 A098494 A008955 * A329120 A152862 A348014

Adjacent sequences: A182821 A182822 A182823 * A182825 A182826 A182827

Keyword

nonn,easy,tabl

Author

Paul Barry, Dec 05 2010

Status

approved