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A293737 Number of multisets of nonempty words with a total of n letters over septenary 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, 1629, 5462, 19164, 69457, 261154, 1012164, 4045640, 16611121, 70001515, 301922104, 1331128134, 5986321599, 27426419974, 127801386949, 605016657100, 2906093083727, 14149469612919, 69762426194708, 348016146152252, 1755188873640756 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence differs from A293110 first at n=8.

LINKS

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

FORMULA

G.f.: Product_{j>=1} 1/(1-x^j)^A007578(j).

MAPLE

g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],

      ((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n+

       305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1)

       *(n-2)*(n-3)*g(n-4))/((n+6)*(n+10)*(n+12)))

    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=7 of A293108.

Cf. A007578, A293110, A293746.

Sequence in context: A018034 A293735 A293736 * A293738 A293739 A293740

Adjacent sequences:  A293734 A293735 A293736 * A293738 A293739 A293740

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 15 2017

STATUS

approved

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Last modified May 21 15:12 EDT 2019. Contains 323444 sequences. (Running on oeis4.)