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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..3163 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 Adjacent sequences: A292546 A292547 A292548 * A292550 A292551 A292552 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 18 2017 STATUS approved

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Last modified August 9 05:47 EDT 2024. Contains 375027 sequences. (Running on oeis4.)