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A292287
Number of multisets of exactly n nonempty balanced binary Lyndon words with a total of 4n letters (2n zeros and 2n ones).
2
1, 1, 4, 12, 43, 142, 508, 1781, 6414, 23124, 84296, 308613, 1137129, 4207456, 15636927, 58322808, 218272766, 819319778, 3083913810, 11636761924, 44010780075, 166802192488, 633420816341, 2409731688860, 9182826866499, 35048239457878, 133965833871427
OFFSET
0,3
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A022553(j+1).
a(n) = A289978(2n,n).
MAPLE
with(numtheory):
g:= proc(n) option remember; `if`(n=0, 1, add(
mobius(n/d)*binomial(2*d, d), d=divisors(n))/(2*n))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(
d*g(d+1), d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30);
MATHEMATICA
g[n_] := g[n] = If[n == 0, 1, Sum[MoebiusMu[n/d] Binomial[2d, d], {d, Divisors[n]}]/(2n)];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*g[d+1], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 23 2023, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A149354 A197659 A360468 * A003444 A220881 A149355
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 20 2017
STATUS
approved