A301270 - OEIS

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A301270

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

4, 20, 144, 1372, 16384, 236196, 4000000, 77948684, 1719926784, 42417997492, 1157018619904, 34599023437500, 1125899906842624, 39618312131623748, 1499253470328324096, 60724508119499193196, 2621440000000000000000, 120167769980326767578964, 5829995856912430117421056, 298461883710362842247633948, 16079954871362414694843285504

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,1

LINKS

Table of n, a(n) for n=4..24.

M. Lavrov and M. Riedel, math.stackexchange.com, Number of labelled trees on n vertices containing two fixed non-adjacent edges

FORMULA

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

EXAMPLE

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).

MATHEMATICA

Array[4 #^(# - 4) &, 21, 4] (* Michael De Vlieger, Mar 19 2018 *)