OFFSET
0,2
COMMENTS
a(n) appears as coefficient of x^(2*n)/n! in the expansion of 1/sqrt(1-4*x^2). - Wolfdieter Lang, Oct 06 2008
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..202
R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Q_{8n+1}, Eq. (22))
FORMULA
a(n) - 4*(2*n-1)^2*a(n-1) = 0. - R. J. Mathar, Apr 02 2017
From Amiram Eldar, May 17 2022: (Start)
Sum_{n>=0} 1/a(n) = 1 + L_0(1/2)*Pi/4, where L is the modified Struve function.
Sum_{n>=0} (-1)^n/a(n) = 1 - H_0(1/2)*Pi/4, where H is the Struve function. (End)
EXAMPLE
a(n)= ((2*n)!/n!)^2 = A001813(n)^2. - Wolfdieter Lang, Oct 06 2008
MAPLE
Q:=proc(n) local m; if n mod 8 <> 1 then RETURN(0); fi; m:=(n-1)/8; ((2*m)!)^2/(m!)^2; end;
MATHEMATICA
Array[((2#)!/#!)^2 &, 15, 0] (* Amiram Eldar, Dec 16 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 25 2006
STATUS
approved