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%I #74 Oct 30 2024 11:34:45
%S 12,32,168,1152,9600,97920,1491840,21127680,377395200,7605964800,
%T 164457216000,3935477145600,102571486617600,2858053098700800,
%U 85725900868608000,2745404797943808000,93266934645620736000,3356738924418367488000,127589166595209166848000
%N Number of graceful labelings for the complete tripartite graph K_{1,1,n}.
%C Except for n = 2, a(n) = A333728(n+2) up to at least n = 6.
%H Paolo Xausa, <a href="/A334307/b334307.txt">Table of n, a(n) for n = 1..400</a> (terms 1..48 from Don Knuth)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a>
%F If n>1, a(n) = 4*A339891(n)*n!. - _Don Knuth_, Dec 21 2020.
%t A334307[n_]:=If[n==1,12,4n!(DivisorSum[2n+1,2^((#-1)/2)&]+DivisorSigma[0,n+1]-2^(n-1)-1)];Array[A334307, 25] (* _Paolo Xausa_, Dec 04 2023 *)
%Y Cf. A333728 (maximum number of graceful labelings for an n-node simple graph), A339891.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Apr 24 2020
%E a(8) and a(9) from _Pontus von Brömssen_, Jul 25 2020
%E Terms a(10) and beyond from _Don Knuth_, Dec 21 2020