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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). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Paul Barry, Dec 05 2010
STATUS
approved

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Last modified April 20 15:27 EDT 2024. Contains 371844 sequences. (Running on oeis4.)