%I #11 Jun 16 2017 03:50:18

%S 1,1,3,9,31,112,467,2141,10739,58454,340389,2110093,13830234,95475087,

%T 691543059,5240282987,41432986587,341040306207,2916376237349,

%U 25862097428262,237434959190586,2253358056942644,22076003468637449,222979436688500085,2319295172178428701

%N Number of primitive (aperiodic) reversible string structures with n beads using an infinite alphabet.

%H Andrew Howroyd, <a href="/A276549/b276549.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = Sum_{d|n} mu(n/d) * A103293(d+1).

%t b[n_] := SeriesCoefficient[Exp[(Exp[2*x] - 3)/2 + Exp[x]], {x, 0, n}]*n!;

%t c[n_] := If[n == 0, 1, (BellB[n - 1] + If[Mod[n, 2] == 1, b[(n - 1)/2], Sum[Binomial[n/2 - 1, k]*b[k], {k, 0, n/2 - 1}]])/2];

%t a[n_] := DivisorSum[n, MoebiusMu[n/#] c[# + 1]&];

%t Array[a, 25] (* _Jean-François Alcover_, Jun 16 2017, using _Alois P. Heinz_'s code for A103293 *)

%Y Row sums of A276544.

%Y Cf. A103293.

%K nonn

%O 1,3

%A _Andrew Howroyd_, Apr 09 2017