cp's OEIS Frontend

A302750 Number of maximum matchings in the n-path complement graph.

%I A302750 #18 Feb 16 2025 08:33:53
%S A302750 1,1,1,1,6,5,41,36,365,329,3984,3655,51499,47844,769159,721315,
%T A302750 13031514,12310199,246925295,234615096,5173842311,4939227215,
%U A302750 118776068256,113836841041,2964697094281,2850860253240,79937923931761,77087063678521,2315462770608870,2238375706930349
%N A302750 Number of maximum matchings in the n-path complement graph.
%C A302750 Except for n=2, the number of edges in a maximum matching is floor(n/2). - _Andrew Howroyd_, Apr 15 2018
%H A302750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>
%H A302750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>
%F A302750 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
%F A302750 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
%t A302750 Join[{1, 1}, Table[(2^-Floor[n/2] n! Hypergeometric1F1[-Floor[n/2], -n, -2])/Floor[n/2]!, {n, 3, 30}]]
%o A302750 (PARI)
%o A302750 b(n)=(2*n)!/(2^n*n!);
%o A302750 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
%Y A302750 Cf. A170941 (matchings), A302749 (maximal matchings).
%K A302750 nonn
%O A302750 1,5
%A A302750 _Eric W. Weisstein_, Apr 12 2018
%E A302750 a(17)-a(30) from _Andrew Howroyd_, Apr 15 2018