A213937 Row sums a(n) of triangle A213936: number of representative necklaces with n beads (C_N symmetry) corresponding to all color signatures given by the partitions [1^n], [2,1^(n-2)], ..., [n-1,1], [n].

1, 2, 4, 11, 42, 207, 1238, 8661, 69282, 623531, 6235302, 68588313, 823059746, 10699776687, 149796873606, 2246953104077, 35951249665218, 611171244308691, 11001082397556422, 209020565553572001

Offset

1,2

Comments

See A213936 and A212359 for more details, references and links.

Links

Table of n, a(n) for n=1..20.

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

Cf. A002627, A231936, A248669.

Sequence in context: A099934 A067353 A105996 * A328437 A107703 A140838

Adjacent sequences: A213934 A213935 A213936 * A213938 A213939 A213940

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 10 2012

Status

approved