A320206 - OEIS

%I #8 Oct 07 2018 14:44:04

%S 501,9945,121710,1185360,10096795,78808600,578849355,4067705855,

%T 27649153955,183168119565,1189058740200,7593928600995,47855567247145,

%U 298255270385350,1841612720379730,11281413505991390,68637389125392080,415119249476398580,2497526622600665470

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

%H Alois P. Heinz, <a href="/A320206/b320206.txt">Table of n, a(n) for n = 5..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))(5):

%p seq(a(n), n=5..25);

%Y Column k=5 of A319501.

%Y Cf. A320215.

%K nonn

%O 5,1

%A _Alois P. Heinz_, Oct 07 2018