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A316410 Number of multisets of exactly nine nonempty binary words with a total of n letters such that no word has a majority of 0's. 2
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17188, 45684, 120435, 313280, 808581, 2065885, 5241557, 13191343, 32992806, 81964072, 202499115, 497418503, 1215823396, 2956890329, 7159215090, 17256728038, 41428552721, 99060756883, 235997525351, 560191343126 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..1000

FORMULA

a(n) = [x^n y^9] 1/Product_{j>=1} (1-y*x^j)^A027306(j).

MAPLE

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

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

       binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 10)

    end:

a:= n-> coeff(b(n$2), x, 9):

seq(a(n), n=9..37);

CROSSREFS

Column k=9 of A292506.

Cf. A027306, A292549.

Sequence in context: A316407 A316408 A316409 * A316411 A292549 A062454

Adjacent sequences:  A316407 A316408 A316409 * A316411 A316412 A316413

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 02 2018

STATUS

approved

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Last modified December 6 01:25 EST 2021. Contains 349558 sequences. (Running on oeis4.)