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%I #10 Sep 03 2017 11:29:23
%S 1,4,20,145,1441,18248,280392,5063361,105063361,2463011052,
%T 64380375276,1856540769313,58550453144609,2004745521503984,
%U 74062339559431920,2936485391069247713,124376016487663499489,5604762874272465685428
%N Number of labeled trees on <= n nodes.
%C 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.
%F a(n) = Sum_{k=2..n} k^(k-2). a(n) = Sum_{k=2..n} A000272(k).
%p a:=n->sum ((j+2)^j, j=0..n): seq(a(n), n=0..17); # _Zerinvary Lajos_, Dec 17 2008
%t Table[Sum[k^(k-2),{k,2,n}],{n,2,25}] (* _Harvey P. Dale_, Jul 11 2011 *)
%Y Cf. A000178, A000272, A001923, A061789.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, May 03 2006
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