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A293738
Number of multisets of nonempty words with a total of n letters over octonary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
5
1, 1, 3, 7, 20, 54, 164, 500, 1630, 5471, 19246, 70020, 264961, 1035540, 4187725, 17440159, 74817905, 329400093, 1487844185, 6873585346, 32460719143, 156315314070, 767106102127, 3828629444020, 19423438144438, 99998608025751, 522200287437179, 2762351298913471
OFFSET
0,3
COMMENTS
This sequence differs from A293110 first at n=9.
LINKS
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A007580(j).
a(n) ~ c * 8^n / n^14, where c = 4485962145436.6348123684794... - Vaclav Kotesovec, Dec 19 2020
MAPLE
g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
((40*n^3+1084*n^2+8684*n+18480)*g(n-1) +16*(n-1)*
(5*n^3+107*n^2+610*n+600)*g(n-2) -1024*(n-1)*(n-2)*
(n+6)*g(n-3) -1024*(n-1)*(n-2)*(n-3)*(n+4)*g(n-4))
/((n+7)*(n+12)*(n+15)*(n+16)))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(g(d)
*d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
CROSSREFS
Column k=8 of A293108.
Sequence in context: A293735 A293736 A293737 * A293739 A293740 A293110
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2017
STATUS
approved