%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