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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

%I

%S 6,48,274,1338,6035,25874,108002,444458,1818905,7451418,30693022,

%T 127604480,536876960,2291507552,9939572897,43885543586,197465168488,

%U 906430558822,4247727231198,20333276583188,99450038211268,497066503157976,2538584563166367

%N 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.

%H Alois P. Heinz, <a href="/A293967/b293967.txt">Table of n, a(n) for n = 11..807</a>

%F a(n) = [x^n y^5] Product_{j>=1} (1+y*x^j)^A000085(j).

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

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

%p add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 6)

%p end:

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

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

%Y Column k=5 of A293815.

%Y Cf. A000085.

%K nonn

%O 11,1

%A _Alois P. Heinz_, Oct 20 2017

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Last modified May 25 12:34 EDT 2022. Contains 354071 sequences. (Running on oeis4.)