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A174558 Number of ways to place 8n nonattacking kings on a 16 x 2n chessboard.

%I A174558 #28 Aug 31 2024 15:01:20
%S A174558 2304,419933,28432288,1134127305,32580145116,749160010737,
%T A174558 14677177838054,254977173389319,4035559337688370,59315924213143597,
%U A174558 821112680030028632,10819171744710664383,136800806311499633208,1670597119210336446533,19804685547188544317522,228865023358344707514899,2586924156960003793687130,28681715460054576813151389,312656761422008821513384848,3357651442822195404605813501
%N A174558 Number of ways to place 8n nonattacking kings on a 16 x 2n chessboard.
%H A174558 Vaclav Kotesovec, <a href="/A174558/b174558.txt">Table of n, a(n) for n = 1..1000</a>
%H A174558 Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013
%H A174558 Vaclav Kotesovec, <a href="/A174558/a174558.txt">G.f.</a>
%H A174558 <a href="/index/Rec#order_307">Index entries for linear recurrences with constant coefficients</a>, order 307.
%F A174558 Asymptotic formula for number of ways to place m x n nonattacking kings on a 2m x 2n chessboard (this case is m=8): f(m,n) ~ k(m)*n*(m+1)^n
%F A174558 First values of k(m):
%F A174558 k(1)=1,
%F A174558 k(2)=17,
%F A174558 k(3)=231,
%F A174558 k(4)=3051.17509,
%F A174558 k(5)=40881.99638,
%F A174558 k(6)=563050.92363,
%F A174558 k(7)=8008508.28858,
%F A174558 k(8)=117833087.45133
%F A174558 k(9)=1794306724.77472
%F A174558 k(10)=28276454469.76459
%F A174558 k(11)=461049875818.05305
%F A174558 k(12)=7775513990776.97046
%F A174558 k(13)=135589372611110.17367
%F A174558 k(14)=2443990803097108.58764
%F A174558 k(15)=45522076785406201.22572
%F A174558 k(16)=875939597341977670.66777
%F A174558 k(17)=17407856624734801679.11613
%F A174558 k(18)=357216046100723515478.42809
%F A174558 k(19)=7567101689641721175327.80272
%Y A174558 Column k=8 of A350819.
%Y A174558 Cf. A174155, A174154, A173782, A173783, A061594, A061593, A018807.
%K A174558 nonn
%O A174558 1,1
%A A174558 _Vaclav Kotesovec_, Nov 29 2010