A095338 Total number of leaves in the labeled graphs of order n.
0, 2, 12, 96, 1280, 30720, 1376256, 117440512, 19327352832, 6184752906240, 3870280929771520, 4755801206503243776, 11510768301994760208384, 55006124792465627449131008, 519934816499859715457632174080, 9735556609752801803494680617287680, 361550014853497117429835520396253724672
Offset: 1
Examples
G.f. = 2*x^2 + 12*x^3 + 96*x^4 + 1280*x^5 + 30720*x^6 + 1376256*x^7 + ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..80
- Eric Weisstein's World of Mathematics, Tree Leaf
Crossrefs
Cf. A182166.
Programs
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Magma
[n*(n-1)*2^Binomial(n-1, 2): n in [1..20]]; // Vincenzo Librandi, Mar 14 2014
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Maple
A095338:=n->n*(n-1)*2^binomial(n-1,2): seq(A095338(n), n=1..20); # Wesley Ivan Hurt, Oct 17 2014
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Mathematica
Table[n (n - 1) 2^(Binomial[n-1, 2]), {n, 20}] (* Vincenzo Librandi, Mar 14 2014 *) -
PARI
a(n) = n*(n-1)*2^binomial(n-1,2); \\ Joerg Arndt, Mar 12 2014
Formula
Conjecture: a(n) = n*(n-1)*2^binomial(n-1,2). - Vladeta Jovovic, Jan 26 2006
a(n) = n*(n-1)*2^binomial(n-1,2) is correct, since counting the total number of leaves in the labeled graphs of order n is equivalent to counting all labeled rooted graphs of order n where the root is a leaf. - Bertran Steinsky, Mar 04 2014
a(n) = 2^(n-1) * A182166(n) for n>=2. - Joerg Arndt, Mar 12 2014
Comments