A117887 Number of labeled trees on <= n nodes.

1, 4, 20, 145, 1441, 18248, 280392, 5063361, 105063361, 2463011052, 64380375276, 1856540769313, 58550453144609, 2004745521503984, 74062339559431920, 2936485391069247713, 124376016487663499489, 5604762874272465685428

Offset: 1

Author

Jonathan Vos Post, May 03 2006

Keywords

• easy
• nonn

Comments

A000178 = Sum_{k=1..n} k^(k-1). A001923 = Sum_{k=1..n} k^k. A061789 = Sum_{k=1..n} p(k)^p(k), p(k) = k-th prime. a(n) = number of spanning trees in complete graphs K_i on i <= n labeled nodes. Also is partial sum of counts of parking functions, noncrossing partitions, critical configurations of the chip firing game, allowable pairs sorted by a priority queue. a(14) = 58550453144609 is prime.

Crossrefs

Cf. A000178, A000272, A001923, A061789.

Programs

Maple

a:=n->sum ((j+2)^j, j=0..n): seq(a(n), n=0..17); # Zerinvary Lajos, Dec 17 2008

Mathematica

Table[Sum[k^(k-2),{k,2,n}],{n,2,25}] (* Harvey P. Dale, Jul 11 2011 *)

Formula

a(n) = Sum_{k=2..n} k^(k-2). a(n) = Sum_{k=2..n} A000272(k).