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%I #11 Feb 20 2021 00:37:26
%S 0,0,0,4,49,481,4681,47881,524161,6168961,78019201,1057795201,
%T 15328051201,236626790401,3879433958401,67345229952001,
%U 1234444603392001,23831057682432001,483379214782464001,10279010984546304001
%N a(n) = (1/4)*(n^2 - 5*n + 2)*(n-2)! + 1.
%C Genera of curves B whose function field K(B) is Galois closure [Galois closed, perhaps? - _N. J. A. Sloane_, Feb 08 2010].
%C a(n) is also the cyclomatic number of the (n-2)-transposition graph. - _Eric W. Weisstein_, Apr 03 2017
%D Nils Bruin and Noam D. Elkies, Trinomials ax^7+bx+c and ax^8+bx+c with Galois Groups of Order 168 and 8*168, in Claus Fieker, David R. Kohel (Editors): Algorithmic Number Theory, 5th International Symposium, ANTS-V, Lecture Notes in Computer Science 2369 Springer 2002, pp. 172 - 188.
%H G. C. Greubel, <a href="/A173038/b173038.txt">Table of n, a(n) for n = 2..445</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclomaticNumber.html">Cyclomatic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TranspositionGraph.html">Transposition Graph</a>
%F E.g.f.: ( -4 +2*x +3*x^2 +4*(1-x)*exp(x) +2*(1-x^2)*log(1-x) )/(4*(1-x)). - _G. C. Greubel_, Feb 19 2021
%p A173038:= n-> (1/4)*(n^2 -5*n +2)*(n-2)! + 1; seq(A173038(n), n=2..30) # _G. C. Greubel_, Feb 19 2021
%t Table[(1/4)*(n^2 -5*n +2)*(n-2)! + 1, {n, 2, 30}]
%o (Sage) [(1/4)*(n^2 -5*n +2)*factorial(n-2) + 1 for n in (2..30)] # _G. C. Greubel_, Feb 19 2021
%o (Magma) [(1/4)*(n^2 -5*n +2)*Factorial(n-2) + 1: n in [2..30]]; // _G. C. Greubel_, Feb 19 2021
%K nonn
%O 2,4
%A _Artur Jasinski_, Feb 08 2010
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