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A292548
Number of multisets of nonempty binary words with a total of n letters such that no word has a majority of 0's.
3
1, 1, 4, 8, 25, 53, 148, 328, 858, 1938, 4862, 11066, 27042, 61662, 147774, 336854, 795678, 1810466, 4228330, 9597694, 22211897, 50279985, 115489274, 260686018, 594986149, 1339215285, 3040004744, 6823594396, 15416270130, 34510814918, 77644149076, 173368564396
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A027306(j).
Euler transform of A027306.
EXAMPLE
a(0) = 1: {}.
a(1) = 1: {1}.
a(2) = 4: {01}, {10}, {11}, {1,1}.
a(3) = 8: {011}, {101}, {110}, {111}, {1,01}, {1,10}, {1,11}, {1,1,1}.
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), 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], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 30 2022, after Alois P. Heinz *)
CROSSREFS
Row sums of A292506.
Column k=2 of A292712.
Cf. A027306.
Sequence in context: A371190 A185615 A068367 * A000964 A297458 A328038
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 18 2017
STATUS
approved