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Number of labeled trees on n vertices containing two fixed non-adjacent edges.
0

%I #18 Apr 15 2018 18:48:19

%S 4,20,144,1372,16384,236196,4000000,77948684,1719926784,42417997492,

%T 1157018619904,34599023437500,1125899906842624,39618312131623748,

%U 1499253470328324096,60724508119499193196,2621440000000000000000,120167769980326767578964,5829995856912430117421056,298461883710362842247633948,16079954871362414694843285504

%N Number of labeled trees on n vertices containing two fixed non-adjacent edges.

%H M. Lavrov and M. Riedel, math.stackexchange.com, <a href="https://math.stackexchange.com/questions/2691262/">Number of labelled trees on n vertices containing two fixed non-adjacent edges</a>

%F a(n) = 0 for n < 4, 4 * n^(n-4) = 4 * A008785(n-4) otherwise.

%e The edges {1,2} and {3,4} can form a tree by being joined by an edge in four ways (two possibilities for each edge).

%t Array[4 #^(# - 4) &, 21, 4] (* _Michael De Vlieger_, Mar 19 2018 *)

%Y Cf. A000169, A000272, A008785.

%K nonn

%O 4,1

%A _Marko Riedel_, Mar 17 2018