A302749 - OEIS

%I #13 Apr 16 2018 18:44:16

%S 1,1,1,2,6,11,41,77,365,694,3984,7639,51499,99343,769159,1490474,

%T 13031514,25341713,246925295,481540391,5173842311,10113069526,

%U 118776068256,232612909297,2964697094281,5815557347521,79937923931761,157024987610282,2315462770608870,4553838477539219

%N Number of maximal matchings in the n-path complement graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>

%F a(2n+1) = A302750(2n+1), a(2n) = Sum_{k=0..n} (1-k)*(-1)^k*binomial(2*n-k,k)*(2*(n-k)-1)!!. - _Andrew Howroyd_, Apr 15 2018

%t Table[If[Mod[n, 2] == 0, (n - 1)!! (Hypergeometric1F1[1 - n/2, 1 - n, -2] + Hypergeometric1F1[-n/2, -n, -2]), (2^-Floor[n/2] n! Hypergeometric1F1[-Floor[n/2], -n, -2])/Floor[n/2]!], {n, 30}]

%o (PARI)

%o b(n)=(2*n)!/(2^n*n!);

%o a(n)=sum(k=0, n\2, if(n%2,1,(1-k))*(-1)^k*binomial(n-k,k)*b((n+1)\2-k)) \\ _Andrew Howroyd_, Apr 15 2018

%Y Cf. A170941 (matchings), A302750 (maximum matchings).

%K nonn

%O 1,4

%A _Eric W. Weisstein_, Apr 12 2018

%E a(17)-a(30) from _Andrew Howroyd_, Apr 15 2018