OFFSET
1,3
COMMENTS
The first 11 terms of this sequence are the same as A317527. - Andrew Howroyd, Jul 30 2018
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = n! * (A013939(n) - floor((n + 2)/4)) / 2. - Andrew Howroyd, Jul 30 2018
PROG
(GAP) List([1..7], n->Sum(Filtered( ConjugacyClassesSubgroups( AlternatingGroup(n)), x->IsPrime( Size( Representative(x))) ), x->Size(x)*Size( Normalizer( AlternatingGroup(n), Representative(x))) )); # Andrew Howroyd, Jul 30 2018
(GAP)
a:=function(n) local total, perm, g, p, k;
total:= 0; g:= AlternatingGroup(n);
for p in Filtered([2..n], IsPrime) do for k in [1..QuoInt(n, p)] do
if p>2 or IsEvenInt(k) then
perm:=PermList(List([0..p*k-1], i->i - (i mod p) + ((i + 1) mod p) + 1));
total:=total + Size(Normalizer(g, perm)) * Factorial(n) / (p^k * (p-1) * Factorial(k) * Factorial(n-k*p));
fi;
od; od;
return total;
end; # Andrew Howroyd, Jul 30 2018
(PARI) a(n)={n!*sum(p=2, n, if(isprime(p), if(p==2, n\4, n\p)))/2} \\ Andrew Howroyd, Jul 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Apr 04 2012
EXTENSIONS
Some incorrect conjectures removed by Andrew Howroyd, Jul 30 2018
Terms a(9) and beyond from Andrew Howroyd, Jul 30 2018
STATUS
approved