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.

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

Author

Alois P. Heinz, Sep 18 2017

Keywords

• nonn

Examples

			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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3163

Crossrefs

Cf. A292506.

Programs

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 *)

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).