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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)