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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3213

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);

CROSSREFS

Row sums of A292506.

Column k=2 of A292712.

Cf. A027306.

Sequence in context: A154586 A185615 A068367 * A000964 A297458 A328038

Adjacent sequences:  A292545 A292546 A292547 * A292549 A292550 A292551

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2017

STATUS

approved

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Last modified September 26 23:32 EDT 2020. Contains 337378 sequences. (Running on oeis4.)