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Number of labeled trees with n nodes and even number of leaves minus number of labeled trees with n nodes and odd number of leaves.
0

%I #4 May 10 2013 12:45:29

%S 1,3,8,5,-156,-1253,48,116937,1236140,-4517689,-317599800,-3473788019,

%T 43408737540,2033846838675,19004486417504,-643679274285679,

%U -24665731809676452,-135665006897593601,15018201730467027960

%N Number of labeled trees with n nodes and even number of leaves minus number of labeled trees with n nodes and odd number of leaves.

%F Sum_{k=0..n} (-1)^k*n!/k!*stirling2(n-2, n-k).

%Y Cf. A055314.

%K sign

%O 2,2

%A _Vladeta Jovovic_, Jan 28 2004