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A293967 Number of sets of exactly five 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
6, 48, 274, 1338, 6035, 25874, 108002, 444458, 1818905, 7451418, 30693022, 127604480, 536876960, 2291507552, 9939572897, 43885543586, 197465168488, 906430558822, 4247727231198, 20333276583188, 99450038211268, 497066503157976, 2538584563166367 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 11..807

FORMULA

a(n) = [x^n y^5] 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, 6)

    end:

a:= n-> coeff(b(n$2), x, 5):

seq(a(n), n=11..35);

CROSSREFS

Column k=5 of A293815.

Cf. A000085.

Sequence in context: A052771 A056289 A056284 * A246587 A340309 A229504

Adjacent sequences:  A293964 A293965 A293966 * A293968 A293969 A293970

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2017

STATUS

approved

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Last modified January 28 12:38 EST 2022. Contains 350656 sequences. (Running on oeis4.)