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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 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

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