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%I #16 Feb 16 2022 23:42:50
%S 1,1,6,576,2073600,498161664000,12385682950717440000,
%T 45484508287062207627264000000,
%U 33297304775599549535597153400913920000000,6298496203530014357849150420174490961843322880000000000,387030157006015555733158587399026951851936435957496524308480000000000000
%N Number of orderings of the edges of the labeled complete graph K_n such that the graph induced by the first k edges is connected for every k=1,2,...,binomial(n,2).
%H G. C. Greubel, <a href="/A255886/b255886.txt">Table of n, a(n) for n = 1..30</a>
%H Mathoverflow, <a href="http://mathoverflow.net/questions/199342">Probability of a graph procedure</a>.
%F For n>1, a(n) = binomial(n,2)! * 2^(n-2) / A000108(n-1).
%t Join[{1}, Table[Binomial[n, 2]!*2^(n-2)*n/Binomial[2*n-2, n-1], {n, 2, 20}]] (* _G. C. Greubel_, Aug 03 2018 *)
%o (PARI) {a(n) = if( n<2, n>0, binomial(n, 2)! * 2^(n-2) * n / binomial(2*n-2, n-1))}; /* _Michael Somos_, Jul 23 2015 */
%o (Magma) [1] cat [Factorial(Binomial(n,2))*2^(n-2)*n/Binomial(2*n-2,n-1): n in [2..20]]; // _G. C. Greubel_, Aug 03 2018
%Y Cf. A125205, A125206, A125207, A125208, A125209.
%K nonn,nice
%O 1,3
%A _Max Alekseyev_, Mar 09 2015
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