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A316407
Number of multisets of exactly six 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, 2284, 6185, 16471, 43156, 111446, 284517, 717486, 1793081, 4434929, 10887761, 26495243, 64069055, 153761086, 366992020, 870215947, 2053484109, 4818104922, 11256015936, 26164409278, 60583174348, 139655557194, 320805463602
OFFSET
6,2
LINKS
FORMULA
a(n) = [x^n y^6] 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, 7)
end:
a:= n-> coeff(b(n$2), x, 6):
seq(a(n), n=6..34);
CROSSREFS
Column k=6 of A292506.
Sequence in context: A333027 A316405 A316406 * A316408 A316409 A316410
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2018
STATUS
approved