%I #8 Oct 07 2018 14:41:31

%S 73,976,8416,59488,375698,2209276,12376430,66974912,353260192,

%T 1827146732,9306483104,46822023764,233203697318,1151770103264,

%U 5647971709608,27525892585476,133427763556914,643682934370820,3091947949892804,14794516505019096,70537743010768506

%N Number of sets of nonempty words with a total of n letters over quaternary alphabet such that all letters occur at least once in the set.

%H Alois P. Heinz, <a href="/A320205/b320205.txt">Table of n, a(n) for n = 4..1000</a>

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

%p add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))

%p end:

%p a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(4):

%p seq(a(n), n=4..30);

%Y Column k=4 of A319501.

%Y Cf. A320214.

%K nonn

%O 4,1

%A _Alois P. Heinz_, Oct 07 2018