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 A316411 Number of multisets of exactly ten nonempty binary words with a total of n letters such that no word has a majority of 0's. 2

%I #9 Jul 02 2018 16:32:17

%S 1,3,10,33,98,291,826,2320,6342,17188,45750,120655,314335,812161,

%T 2078985,5283157,13326283,33400066,83195864,206069915,507722068,

%U 1244740868,3037497201,7379529734,17854498058,43026654989,103302756909,247127149283,589196413579

%N Number of multisets of exactly ten nonempty binary words with a total of n letters such that no word has a majority of 0's.

%H Alois P. Heinz, <a href="/A316411/b316411.txt">Table of n, a(n) for n = 10..1000</a>

%F a(n) = [x^n y^10] 1/Product_{j>=1} (1-y*x^j)^A027306(j).

%p g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):

%p b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(

%p binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 11)

%p end:

%p a:= n-> coeff(b(n\$2), x, 10):

%p seq(a(n), n=10..38);

%Y Column k=10 of A292506.

%Y Cf. A027306, A292549.

%K nonn

%O 10,2

%A _Alois P. Heinz_, Jul 02 2018

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Last modified August 6 06:14 EDT 2024. Contains 374960 sequences. (Running on oeis4.)