This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A095338 #33 Feb 16 2025 08:32:53
%S A095338 0,2,12,96,1280,30720,1376256,117440512,19327352832,6184752906240,
%T A095338 3870280929771520,4755801206503243776,11510768301994760208384,
%U A095338 55006124792465627449131008,519934816499859715457632174080,9735556609752801803494680617287680,361550014853497117429835520396253724672
%N A095338 Total number of leaves in the labeled graphs of order n.
%C A095338 A leaf is defined as a vertex of degree (or valence) 1. - _Michael Somos_, Mar 13 2014
%H A095338 Vincenzo Librandi, <a href="/A095338/b095338.txt">Table of n, a(n) for n = 1..80</a>
%H A095338 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TreeLeaf.html">Tree Leaf</a>
%F A095338 Conjecture: a(n) = n*(n-1)*2^binomial(n-1,2). - _Vladeta Jovovic_, Jan 26 2006
%F A095338 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
%F A095338 a(n) = 2^(n-1) * A182166(n) for n>=2. - _Joerg Arndt_, Mar 12 2014
%e A095338 G.f. = 2*x^2 + 12*x^3 + 96*x^4 + 1280*x^5 + 30720*x^6 + 1376256*x^7 + ...
%p A095338 A095338:=n->n*(n-1)*2^binomial(n-1,2): seq(A095338(n), n=1..20); # _Wesley Ivan Hurt_, Oct 17 2014
%t A095338 Table[n (n - 1) 2^(Binomial[n-1, 2]), {n, 20}] (* _Vincenzo Librandi_, Mar 14 2014 *)
%o A095338 (PARI) a(n) = n*(n-1)*2^binomial(n-1,2); \\ _Joerg Arndt_, Mar 12 2014
%o A095338 (Magma) [n*(n-1)*2^Binomial(n-1, 2): n in [1..20]]; // _Vincenzo Librandi_, Mar 14 2014
%Y A095338 Cf. A182166.
%K A095338 nonn,easy
%O A095338 1,2
%A A095338 _Eric W. Weisstein_, Jun 02 2004