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 A095338 Total number of leaves in the labeled graphs of order n. 3
 0, 2, 12, 96, 1280, 30720, 1376256, 117440512, 19327352832, 6184752906240, 3870280929771520, 4755801206503243776, 11510768301994760208384, 55006124792465627449131008, 519934816499859715457632174080, 9735556609752801803494680617287680, 361550014853497117429835520396253724672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A leaf is defined as a vertex of degree (or valence) 1. - Michael Somos, Mar 13 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..80 Eric Weisstein's World of Mathematics, Tree Leaf 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 EXAMPLE G.f. = 2*x^2 + 12*x^3 + 96*x^4 + 1280*x^5 + 30720*x^6 + 1376256*x^7 + ... MAPLE A095338:=n->n*(n-1)*2^binomial(n-1, 2): seq(A095338(n), n=1..20); # Wesley Ivan Hurt, Oct 17 2014 MATHEMATICA Table[n (n - 1) 2^(Binomial[n-1, 2]), {n, 20}] (* Vincenzo Librandi, Mar 14 2014 *) PROG (PARI) a(n) = n*(n-1)*2^binomial(n-1, 2); \\ Joerg Arndt, Mar 12 2014 (MAGMA) [n*(n-1)*2^Binomial(n-1, 2): n in [1..20]]; // Vincenzo Librandi, Mar 14 2014 CROSSREFS Cf. A182166. Sequence in context: A052611 A340938 A059864 * A308820 A322717 A219538 Adjacent sequences:  A095335 A095336 A095337 * A095339 A095340 A095341 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jun 02 2004 STATUS approved

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Last modified August 4 14:28 EDT 2021. Contains 346447 sequences. (Running on oeis4.)