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%I #15 Apr 05 2022 21:26:47
%S 1,2,4,11,42,207,1238,8661,69282,623531,6235302,68588313,823059746,
%T 10699776687,149796873606,2246953104077,35951249665218,
%U 611171244308691,11001082397556422,209020565553572001
%N 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].
%C See A213936 and A212359 for more details, references and links.
%F a(n) = A002627(n-1) + 1, n>=1.
%F a(n) = Sum_{k=1..n} A213936(n,k), n>=1.
%F a(n) = 1 + Sum_{k=1..n-1} (n-1)!/k! = 1 + A002627(n-1), n>=1.
%F a(n) = 1 + Sum_{k=1..n} A248669(n-1,k), n>=1. - _Greg Dresden_, Mar 31 2022
%e 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).
%Y Cf. A002627, A231936, A248669.
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Jul 10 2012
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