OFFSET
0,5
COMMENTS
Inverse is A182822.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)
FORMULA
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)].
EXAMPLE
Triangle begins
1,
-1, 1,
1, -3, 1,
1, 6, -6, 1,
-13, 4, 21, -10, 1,
49, -129, -5, 55, -15, 1,
31, 723, -624, -85, 120, -21, 1,
-1981, -386, 5271, -2009, -385, 231, -28, 1,
14329, -34320, -11978, 25508, -4809, -1204, 406, -36, 1
MAPLE
f := proc (n) option remember; normal((x-n)*procname(n-1)-(n-1)^2*procname(n-2)) end proc:
f(0):= 1: f(1):= x-1:
seq(seq(coeff(f(n), x, k), k=0..n), n=0..10); # Robert Israel, Oct 15 2017
MATHEMATICA
(* The function RiordanArray is defined in A256893. *)
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 *)
CROSSREFS
AUTHOR
Paul Barry, Dec 05 2010
STATUS
approved