|
|
A292723
|
|
Number of multisets of nonempty words with a total of n letters over 8-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
|
|
2
|
|
|
1, 1, 4, 14, 67, 343, 2151, 14900, 119259, 692640, 4659774, 30077836, 209311030, 1433872892, 10689029713, 76772260527, 600293120366, 4142024767610, 30775147154084, 221566161988587, 1663421685691847, 12221938274124959, 93706886872251562, 696726353909296853
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{j>=1} 1/(1-x^j)^A226878(j).
|
|
MAPLE
|
b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
b(d, 0, 8), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|