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A293965 Number of sets of exactly three nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 2
1, 8, 30, 114, 411, 1462, 5237, 18998, 70220, 265010, 1024692, 4059100, 16504058, 68843340, 294854550, 1295771712, 5843980456, 27026394156, 128135282356, 622230803212, 3093321051636, 15728089431744, 81739630155456, 433801710925696, 2349410730317456 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..803

FORMULA

a(n) = [x^n y^3] Product_{j>=1} (1+y*x^j)^A000085(j).

MAPLE

g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:

b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,

      add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 4)

    end:

a:= n-> coeff(b(n$2), x, 3):

seq(a(n), n=5..30);

CROSSREFS

Column k=3 of A293815.

Cf. A000085.

Sequence in context: A050477 A239612 A055737 * A161222 A229374 A215471

Adjacent sequences:  A293962 A293963 A293964 * A293966 A293967 A293968

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2017

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)