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A302750
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Number of maximum matchings in the n-path complement graph.
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1
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1, 1, 1, 1, 6, 5, 41, 36, 365, 329, 3984, 3655, 51499, 47844, 769159, 721315, 13031514, 12310199, 246925295, 234615096, 5173842311, 4939227215, 118776068256, 113836841041, 2964697094281, 2850860253240, 79937923931761, 77087063678521, 2315462770608870, 2238375706930349
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OFFSET
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1,5
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COMMENTS
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Except for n=2, the number of edges in a maximum matching is floor(n/2). - Andrew Howroyd, Apr 15 2018
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k,k)*(2*(ceiling(n/2)-k)-1)!! for n > 2. - Andrew Howroyd, Apr 15 2018
a(n) = 2^-floor(n/2)*n!*hypergeometric1f1(-floor(n/2), -n, -2)/(floor(n/2))! for n > 2. - Eric W. Weisstein, Apr 16 2018
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MATHEMATICA
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Join[{1, 1}, Table[(2^-Floor[n/2] n! Hypergeometric1F1[-Floor[n/2], -n, -2])/Floor[n/2]!, {n, 3, 30}]]
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PROG
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(PARI)
b(n)=(2*n)!/(2^n*n!);
a(n)=if(n==2, 1, sum(k=0, n\2, (-1)^k*binomial(n-k, k)*b((n+1)\2-k))); \\ Andrew Howroyd, Apr 15 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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