OFFSET
1,2
COMMENTS
Given 2n vertices, we can choose n-1 of them in C(2n, n-1) ways. For each of these ways there are A000272(n+1) trees. (possibilities)
FORMULA
EXAMPLE
a(1) = 1. The forest is the tree of 2 nodes. It can be depicted by 1--2.
a(2) = 12. Given 4 nodes we can choose 1 of them in C(4,1) = 4 ways. For each of these 4 ways there are A000272(n+1) = (n+1)^(n-1) = 3 trees to complete the forest. The 12 forests can be represented by:
1 3-2-4, 1 2-3-4, 1 2-4-3,
2 3-1-4, 2 1-3-4, 2 1-4-3,
3 2-1-4, 3 1-2-4, 3 1-4-2,
4 2-1-3, 4 1-2-3, 4 1-3-2.
MATHEMATICA
a[n_] := Binomial[2n, n-1] * (n+1)^(n-1); Array[a, 18] (* Amiram Eldar, Apr 12 2020 *)
PROG
(PARI) a(n) = binomial(2*n, n-1) * (n+1)^(n-1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Washington Bomfim, Apr 12 2020
STATUS
approved