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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).

%I A182824 #13 Oct 15 2024 23:16:29
%S A182824 1,1,1,5,4,1,21,33,9,1,153,264,114,16,1,1209,2769,1410,290,25,1,12285,
%T A182824 32076,20259,5040,615,36,1,140589,432657,314811,94899,14175,1155,49,1,
%U A182824 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
%N 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).
%C A182824 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).
%C A182824 Inverse is A182826. First column is A182825.
%F A182824 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))].
%e A182824 Triangle begins:
%e A182824   1,
%e A182824   1, 1,
%e A182824   5, 4, 1,
%e A182824   21, 33, 9, 1,
%e A182824   153, 264, 114, 16, 1,
%e A182824   1209, 2769, 1410, 290, 25, 1,
%e A182824   12285, 32076, 20259, 5040, 615, 36, 1,
%e A182824   140589, 432657, 314811, 94899, 14175, 1155, 49, 1,
%e A182824   1871217, 6475536, 5423076, 1886304, 337974, 33936, 1988, 64, 1
%e A182824 Production matrix begins:
%e A182824   1, 1,
%e A182824   4, 3, 1,
%e A182824   0, 16, 5, 1,
%e A182824   0, 0, 36, 7, 1,
%e A182824   0, 0, 0, 64, 9, 1,
%e A182824   0, 0, 0, 0, 100, 11, 1,
%e A182824   0, 0, 0, 0, 0, 144, 13, 1,
%e A182824   0, 0, 0, 0, 0, 0, 196, 15, 1,
%e A182824   0, 0, 0, 0, 0, 0, 0, 256, 17, 1
%e A182824   0, 0, 0, 0, 0, 0, 0, 0, 324, 19, 1
%t A182824 (* The function RiordanArray is defined in A256893. *)
%t A182824 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 *)
%K A182824 nonn,easy,tabl
%O A182824 0,4
%A A182824 _Paul Barry_, Dec 05 2010