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A244288 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected nw-se.

%I A244288 #14 Mar 27 2023 22:37:07
%S A244288 1,1,5,57,1084,29003,999717,42125233,2096106904,120194547233,
%T A244288 7799803041491,564856080384900,45146219773912540,3946445378386791157,
%U A244288 374482268128153003615,38330653031858936914329,4209191997519328986666624,493575737047609363968826907
%N A244288 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected nw-se.
%H A244288 Andrew Howroyd, <a href="/A244288/b244288.txt">Table of n, a(n) for n = 0..200</a>
%H A244288 Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p.422
%F A244288 a(n) ~ n^(2*n)/n! * exp(-3/2).
%o A244288 (PARI) P(m,n) = sum(k=0, (m+1)\2, binomial(m-k+1,k)*x^k, O(x*x^n))
%o A244288 a(n) = polcoef(P(n,n)*prod(m=1, n-1, P(m,n))^2, n) \\ _Andrew Howroyd_, Mar 27 2023
%Y A244288 Cf. A197989, A201540, A201511, A201861, A201513, A244284.
%K A244288 nonn
%O A244288 0,3
%A A244288 _Vaclav Kotesovec_, Jun 25 2014
%E A244288 a(16) from _Vaclav Kotesovec_, Sep 04 2016
%E A244288 a(17) from _Vaclav Kotesovec_, Jun 15 2021
%E A244288 a(0)=1 prepended by _Andrew Howroyd_, Mar 27 2023