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A276549 Number of primitive (aperiodic) reversible string structures with n beads using an infinite alphabet. 2
1, 1, 3, 9, 31, 112, 467, 2141, 10739, 58454, 340389, 2110093, 13830234, 95475087, 691543059, 5240282987, 41432986587, 341040306207, 2916376237349, 25862097428262, 237434959190586, 2253358056942644, 22076003468637449, 222979436688500085, 2319295172178428701 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{d|n} mu(n/d) * A103293(d+1).
MATHEMATICA
b[n_] := SeriesCoefficient[Exp[(Exp[2*x] - 3)/2 + Exp[x]], {x, 0, n}]*n!;
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];
a[n_] := DivisorSum[n, MoebiusMu[n/#] c[# + 1]&];
Array[a, 25] (* Jean-François Alcover, Jun 16 2017, using Alois P. Heinz's code for A103293 *)
CROSSREFS
Row sums of A276544.
Cf. A103293.
Sequence in context: A056334 A063032 A056335 * A049188 A049165 A052709
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 09 2017
STATUS
approved

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Last modified February 21 15:59 EST 2024. Contains 370237 sequences. (Running on oeis4.)