A182826 Coefficient array for orthogonal polynomials p(n,x)=(x-(2n-1))*p(n-1,x)-(2n-2)^2*p(n-2,x), p(0,x)=1,p(1,x)=x-1.

1, -1, 1, -1, -4, 1, 21, 3, -9, 1, -111, 144, 30, -16, 1, -345, -1599, 450, 110, -25, 1, 14895, 2844, -9549, 840, 285, -36, 1, -143955, 208179, 62181, -36309, 735, 609, -49, 1, -760095, -3824064, 1147068, 442176, -103194, -1344, 1148, -64, 1, 49774095, 10955169, -39242556, 2925180, 2008314, -236250, -8316, 1980, -81, 1, -699437025, 1080622620, 384913701, -238086000

Offset

0,5

Comments

Inverse is A182824. First column is A182827.

Links

Table of n, a(n) for n=0..58.

Formula

Exponential Riordan array [1/sqrt(1+2x+4x^2), arctan(sqrt(3)*x/(1+x))/sqrt(3)].

Example

Triangle begins
1,
-1, 1,
-1, -4, 1,
21, 3, -9, 1,
-111, 144, 30, -16, 1,
-345, -1599, 450, 110, -25, 1,
14895, 2844, -9549, 840, 285, -36, 1,
-143955, 208179, 62181, -36309, 735, 609, -49, 1,
-760095, -3824064, 1147068, 442176, -103194, -1344, 1148, -64, 1

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[1/Sqrt[1 + 2# + 4#^2]&, ArcTan[Sqrt[3] #/(1 + #)]/Sqrt[3]&, 10, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

Crossrefs

Sequence in context: A049352 A322218 A182867 * A144484 A121336 A126457

Adjacent sequences: A182823 A182824 A182825 * A182827 A182828 A182829

Keyword

sign,easy,tabl

Author

Paul Barry, Dec 05 2010

Status

approved