A293736 Number of multisets of nonempty words with a total of n letters over senary 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, 499, 1621, 5397, 18762, 67000, 247439, 936167, 3639968, 14450634, 58677742, 242511781, 1021307520, 4365923278, 18960435664, 83395216882, 371734296357, 1675125941350, 7635063496721, 35127842511275, 163213032700613, 764541230737345

Offset

0,3

Comments

This sequence differs from A293110 first at n=7.

Links

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

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^A007579(j).

a(n) ~ c * 6^n / n^(15/2), where c = 121210.8807171702661881473876689430182129891246619701141888082152779... - Vaclav Kotesovec, May 30 2019

Maple

g:= proc(n) option remember;
      `if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*g(n-1)
       +4*(n-1)*(10*n^2+58*n+33)*g(n-2) -144*(n-1)*(n-2)*g(n-3)
       -144*(n-1)*(n-2)*(n-3)*g(n-4))/ ((n+5)*(n+8)*(n+9)))
    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=6 of A293108.

Cf. A007579, A293110, A293745.

Sequence in context: A293734 A018034 A293735 * A293737 A293738 A293739

Adjacent sequences: A293733 A293734 A293735 * A293737 A293738 A293739

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2017

Status

approved