This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182823 #15 Jul 19 2019 14:26:30 %S A182823 1,-1,1,1,-3,1,1,6,-6,1,-13,4,21,-10,1,49,-129,-5,55,-15,1,31,723, %T A182823 -624,-85,120,-21,1,-1981,-386,5271,-2009,-385,231,-28,1,14329,-34320, %U A182823 -11978,25508,-4809,-1204,406,-36,1,-2177,347913,-263862,-112974,93429,-8757,-3066,666,-45,1,-1138879,-701387,3956751,-1200270,-657735,278523,-10983,-6810,1035,-55,1 %N A182823 Coefficient array of orthogonal polynomials P(n,x)=(x-n)*P(n-1,x)-(n-1)^2*P(n-2,x), P(0,x)=1, P(1,x)=x-1. %C A182823 Inverse is A182822. %H A182823 Robert Israel, <a href="/A182823/b182823.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened) %F A182823 Exponential Riordan array [exp(-arctan(sqrt(3)*x/(x+2))/sqrt(3))/sqrt(1+x+x^2), 2*arctan(sqrt(3)*x/(x+2))/sqrt(3)]. %e A182823 Triangle begins %e A182823 1, %e A182823 -1, 1, %e A182823 1, -3, 1, %e A182823 1, 6, -6, 1, %e A182823 -13, 4, 21, -10, 1, %e A182823 49, -129, -5, 55, -15, 1, %e A182823 31, 723, -624, -85, 120, -21, 1, %e A182823 -1981, -386, 5271, -2009, -385, 231, -28, 1, %e A182823 14329, -34320, -11978, 25508, -4809, -1204, 406, -36, 1 %p A182823 f := proc (n) option remember; normal((x-n)*procname(n-1)-(n-1)^2*procname(n-2)) end proc: %p A182823 f(0):= 1: f(1):= x-1: %p A182823 seq(seq(coeff(f(n),x,k),k=0..n),n=0..10); # _Robert Israel_, Oct 15 2017 %t A182823 (* The function RiordanArray is defined in A256893. *) %t A182823 RiordanArray[Exp[-ArcTan[Sqrt[3]*#/(# + 2)]/Sqrt[3]]/Sqrt[1 + # + #^2]&, 2*ArcTan[Sqrt[3]*#/(# + 2)]/Sqrt[3]&, 10, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *) %K A182823 sign,tabl,look %O A182823 0,5 %A A182823 _Paul Barry_, Dec 05 2010