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%I #9 Feb 23 2023 10:53:45
%S 1,2,6,64,250,1728,67228,2097152,1062882,80000000,9431790764,
%T 6115295232,7168641576148,64793042714624,2562890625000,
%U 1152921504606846976,5724846103019631586,666334875701477376,21921547431139208743756,16777216000000000000000,164839190645167033716,513039635408293850333052928
%N Numerators of Postnikov's hook-length formula 2^n*(n+1)^(n-1)/n!.
%D Alexander Postnikov. Permutohedra, associahedra, and beyond. in: Conference in Honor of Richard Stanley's Sixtieth Birthday, June 2004. International Mathematics Research Notices, 6:1026-1106, 2009.
%H Matthew Wilson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p20">Bruhat order on fixed-point-free involutions in the symmetric group</a>, Electron. J. Combin., 21(2) (2014), #P2.20.
%e 1, 2, 6, 64/3, 250/3, 1728/5, 67228/45, 2097152/315, 1062882/35, 80000000/567, 9431790764/14175, 6115295232/1925, 7168641576148/467775, ...
%p t1:= [seq(2^n*(n+1)^(n-1)/n!,n=0..50)]:
%p t2:=map(numer, t1); # A241590
%p t3:=map(denom, t1); # A241591
%t Join[{1},Table[(2^n (n+1)^(n-1))/n!,{n,30}]//Numerator] (* _Harvey P. Dale_, Feb 23 2023 *)
%o (PARI) vector(30, n, n--; numerator(2^n*(n+1)^(n-1)/n!)) \\ _Michel Marcus_, Jul 18 2015
%Y Cf. A241591.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, May 13 2014
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