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%I #8 Mar 14 2021 18:46:26
%S 1,3,4,72,132,7020,17280,1920240,6022800,1154366640,4421511360,
%T 1303028052480,5906331224640,2481613890275520,13003380449579520,
%U 7385997122881977600,43944212734316294400,32440254625217626387200,216088204725662645376000
%N Number of maximum matchings in the 3 X n rook graph.
%H Andrew Howroyd, <a href="/A341851/b341851.txt">Table of n, a(n) for n = 0..100</a>
%o (PARI) a(n)={my(v=vector((n+1)\2+1, i, i--; (2*i)!/(2^i*i!))); if(n%2,3,1)*sum(i=0, n\2, sum(j=0, n\2, sum(k=abs(i-j), min(i+j, n-i-j), n!/((i+k-j)!*(i+j-k)!*(n-i-j-k)!*(j+k-i)!)*v[1+(n+1)\2-i]*v[1+j]*v[1+k] )))} \\ _Andrew Howroyd_, Mar 14 2021
%Y Row n=3 of A341850.
%Y Cf. A341502, A341848.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Feb 21 2021
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