A058163 Number of labeled groups with a fixed identity.

1, 1, 1, 4, 6, 80, 120, 2760, 7560, 108864, 362880, 21621600, 39916800, 1186099200, 10897286400, 647091244800, 1307674368000, 103742166528000, 355687428096000, 32438693442355200, 260668072304640000, 5573557327822848000, 51090942171709440000

Offset: 1

Author

Christian G. Bower, Nov 15 2000

Keywords

• nonn

Links

• Stephen A. Silver, Table of n, a(n) for n = 1..255
• Index entries for sequences related to groups

Crossrefs

Cf. A000688, A034383, A058158, A058162, A058163.

Programs

GAP

A058163 := function(n) local fn1, sum, k; fn1 := Factorial(n-1); sum := 0; for k in [1 .. NrSmallGroups(n)] do sum := sum + fn1 / Size(AutomorphismGroup(SmallGroup(n,k))); od; return sum; end; # Stephen A. Silver, Feb 10 2013

Formula

a(n) = A034383(n)/n.

Extensions

More terms from Stephen A. Silver, Feb 10 2013