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%I #23 May 17 2022 03:42:27
%S 1,4,144,14400,2822400,914457600,442597478400,299195895398400,
%T 269276305858560000,311283409572495360000,449493243422683299840000,
%U 792906081397613340917760000,1677789268237349829381980160000,4194473170593374573454950400000000,12231083765450280256194635366400000000
%N Bishops on an n X n board (see Robinson paper for details).
%C 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
%H Seiichi Manyama, <a href="/A122747/b122747.txt">Table of n, a(n) for n = 0..202</a>
%H R. W. Robinson, <a href="http://dx.doi.org/10.1007/BFb0097382">Counting arrangements of bishops</a>, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Q_{8n+1}, Eq. (22))
%F a(n) - 4*(2*n-1)^2*a(n-1) = 0. - _R. J. Mathar_, Apr 02 2017
%F From _Amiram Eldar_, May 17 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1 + L_0(1/2)*Pi/4, where L is the modified Struve function.
%F Sum_{n>=0} (-1)^n/a(n) = 1 - H_0(1/2)*Pi/4, where H is the Struve function. (End)
%e a(n)= ((2*n)!/n!)^2 = A001813(n)^2. - _Wolfdieter Lang_, Oct 06 2008
%p Q:=proc(n) local m; if n mod 8 <> 1 then RETURN(0); fi; m:=(n-1)/8; ((2*m)!)^2/(m!)^2; end;
%t Array[((2#)!/#!)^2 &, 15, 0] (* _Amiram Eldar_, Dec 16 2018 *)
%Y Cf. A000984, A001813.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Sep 25 2006
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