OFFSET
1,2
FORMULA
a(n) = A002627(n-1) + 1, n>=1.
a(n) = Sum_{k=1..n} A213936(n,k), n>=1.
a(n) = 1 + Sum_{k=1..n-1} (n-1)!/k! = 1 + A002627(n-1), n>=1.
a(n) = 1 + Sum_{k=1..n} A248669(n-1,k), n>=1. - Greg Dresden, Mar 31 2022
EXAMPLE
n=4: the representative necklaces (of a color class) correspond to the color signatures c[.] c[.] c[.] c[.], c[.]^2 c[.] c[.], c[.]^3 c[.]^1 and c[.]^4 (the reverse partition order compared to Abramowitz-Stegun without 2^2). The corresponding necklaces are (we use j for color c[j]): cyclic(1234), coming in all-together 6 permutations of the present colors, cyclic(1123) coming in 3 permutions, cyclic(1112) and cyclic(1111), adding up to the 11 = a(4) necklaces. Not all 4 colors are present, except for the first signature (partition).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 10 2012
STATUS
approved