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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified May 19 23:16 EDT 2019. Contains 323411 sequences. (Running on oeis4.)