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A122747 Bishops on an n X n board (see Robinson paper for details). 4
1, 4, 144, 14400, 2822400, 914457600, 442597478400, 299195895398400, 269276305858560000, 311283409572495360000, 449493243422683299840000, 792906081397613340917760000, 1677789268237349829381980160000, 4194473170593374573454950400000000, 12231083765450280256194635366400000000 (list; graph; refs; listen; history; text; internal format)
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

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

Cf. A000984, A001813.

Sequence in context: A268894 A084703 A186418 * A069135 A186081 A138176

Adjacent sequences:  A122744 A122745 A122746 * A122748 A122749 A122750

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 25 2006

STATUS

approved

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Last modified October 18 05:14 EDT 2019. Contains 328145 sequences. (Running on oeis4.)