A255886 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).

1, 1, 6, 576, 2073600, 498161664000, 12385682950717440000, 45484508287062207627264000000, 33297304775599549535597153400913920000000, 6298496203530014357849150420174490961843322880000000000, 387030157006015555733158587399026951851936435957496524308480000000000000

Offset: 1

Author

Max Alekseyev, Mar 09 2015

Keywords

• nonn
• nice

Links

• G. C. Greubel, Table of n, a(n) for n = 1..30
• Mathoverflow, Probability of a graph procedure.

Crossrefs

Cf. A125205, A125206, A125207, A125208, A125209.

Programs

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

Mathematica

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 *)

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 */

Formula

For n>1, a(n) = binomial(n,2)! * 2^(n-2) / A000108(n-1).