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.

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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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.

Cf. A007580, A293110, A293747.

Sequence in context: A293735 A293736 A293737 * A293739 A293740 A293110

Adjacent sequences: A293735 A293736 A293737 * A293739 A293740 A293741

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2017

Status

approved