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A292549
Number of multisets of exactly n nonempty binary words with a total of 2n letters such that no word has a majority of 0's.
11
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17188, 45750, 120733, 314690, 813854, 2085363, 5306878, 13406382, 33665476, 84031608, 208655086, 515469203, 1267600993, 3103490884, 7567559622, 18381579206, 44487740012, 107301636460, 257967350824, 618279370985
OFFSET
0,2
LINKS
FORMULA
a(n) = A292506(2n,n) = A292506(2n+j,n+j) for j >= 0.
G.f.: Product_{j>=1} 1/(1-x^j)^A027306(j+1).
Euler transform of j-> A027306(j+1).
EXAMPLE
a(0) = 1: {}.
a(1) = 3: {01}, {10}, {11}.
a(2) = 10: {1,011}, {1,101}, {1,110}, {1,111}, {01,01}, {01,10}, {01,11}, {10,10}, {10,11}, {11,11}.
MAPLE
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
g(d+1), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
MATHEMATICA
g[n_] := 2^(n-1) + If[OddQ[n], 0, Binomial[n, n/2]/2];
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, 35}] (* Jean-François Alcover, May 11 2019, after Alois P. Heinz *)
CROSSREFS
Cf. A292506.
Sequence in context: A316409 A316410 A316411 * A062454 A121523 A115240
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 18 2017
STATUS
approved