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A293735 Number of multisets of nonempty words with a total of n letters over quinary 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, 163, 492, 1571, 5122, 17262, 59483, 209958, 755615, 2770994, 10330036, 39103166, 150073289, 583329574, 2293822828, 9116935874, 36593731182, 148221246775, 605427601519, 2492286544749, 10334197803358, 43140208034891, 181224681022614 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence differs from A293110 first at n=6.

LINKS

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

FORMULA

G.f.: Product_{j>=1} 1/(1-x^j)^A049401(j).

MAPLE

g:= proc(n) option remember;

      `if`(n<3, [1, 1, 2][n+1], ((3*n^2+17*n+15)*g(n-1)

       +(n-1)*(13*n+9)*g(n-2) -15*(n-1)*(n-2)*g(n-3)) /

       ((n+4)*(n+6)))

    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=5 of A293108.

Cf. A049401, A293110, A293744.

Sequence in context: A109220 A293734 A018034 * A293736 A293737 A293738

Adjacent sequences:  A293732 A293733 A293734 * A293736 A293737 A293738

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 15 2017

STATUS

approved

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Last modified May 22 21:17 EDT 2019. Contains 323504 sequences. (Running on oeis4.)