A173038 a(n) = (1/4)*(n^2 - 5*n + 2)*(n-2)! + 1.

0, 0, 0, 4, 49, 481, 4681, 47881, 524161, 6168961, 78019201, 1057795201, 15328051201, 236626790401, 3879433958401, 67345229952001, 1234444603392001, 23831057682432001, 483379214782464001, 10279010984546304001

Offset

2,4

Comments

Genera of curves B whose function field K(B) is Galois closure [Galois closed, perhaps? - N. J. A. Sloane, Feb 08 2010].

a(n) is also the cyclomatic number of the (n-2)-transposition graph. - Eric W. Weisstein, Apr 03 2017

References

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.

Links

G. C. Greubel, Table of n, a(n) for n = 2..445

Eric Weisstein's World of Mathematics, Cyclomatic Number

Eric Weisstein's World of Mathematics, Transposition Graph

Formula

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

Maple

A173038:= n-> (1/4)*(n^2 -5*n +2)*(n-2)! + 1; seq(A173038(n), n=2..30) # G. C. Greubel, Feb 19 2021

Mathematica

Table[(1/4)*(n^2 -5*n +2)*(n-2)! + 1, {n, 2, 30}]

Prog

(Sage) [(1/4)*(n^2 -5*n +2)*factorial(n-2) + 1 for n in (2..30)] # G. C. Greubel, Feb 19 2021
(Magma) [(1/4)*(n^2 -5*n +2)*Factorial(n-2) + 1: n in [2..30]]; // G. C. Greubel, Feb 19 2021

Crossrefs

Sequence in context: A053769 A355481 A362479 * A198971 A348547 A348425

Adjacent sequences: A173035 A173036 A173037 * A173039 A173040 A173041

Keyword

nonn

Author

Artur Jasinski, Feb 08 2010

Status

approved