A122747 Bishops on an n X n board (see Robinson paper for details).

1, 4, 144, 14400, 2822400, 914457600, 442597478400, 299195895398400, 269276305858560000, 311283409572495360000, 449493243422683299840000, 792906081397613340917760000, 1677789268237349829381980160000, 4194473170593374573454950400000000, 12231083765450280256194635366400000000

Offset: 0

Author

N. J. A. Sloane, Sep 25 2006

Keywords

• nonn
• easy

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

Examples

			a(n)= ((2*n)!/n!)^2 = A001813(n)^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))

Crossrefs

Cf. A000984, A001813.

Programs

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 *)

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)