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A320205 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.

%I A320205 #8 Oct 07 2018 14:41:31
%S A320205 73,976,8416,59488,375698,2209276,12376430,66974912,353260192,
%T A320205 1827146732,9306483104,46822023764,233203697318,1151770103264,
%U A320205 5647971709608,27525892585476,133427763556914,643682934370820,3091947949892804,14794516505019096,70537743010768506
%N A320205 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 A320205 Alois P. Heinz, <a href="/A320205/b320205.txt">Table of n, a(n) for n = 4..1000</a>
%p A320205 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A320205       add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
%p A320205     end:
%p A320205 a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(4):
%p A320205 seq(a(n), n=4..30);
%Y A320205 Column k=4 of A319501.
%Y A320205 Cf. A320214.
%K A320205 nonn
%O A320205 4,1
%A A320205 _Alois P. Heinz_, Oct 07 2018