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A320203 Number of sets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the set.

%I A320203 #7 Oct 07 2018 12:04:39
%S A320203 3,12,38,110,302,806,2109,5450,13917,35224,88464,220608,546734,
%T A320203 1347290,3302716,8057268,19568800,47329156,114025658,273709580,
%U A320203 654765164,1561257760,3711372761,8797021430,20794198251,49024480496,115292809466,270495295124,633186396954
%N A320203 Number of sets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the set.
%H A320203 Alois P. Heinz, <a href="/A320203/b320203.txt">Table of n, a(n) for n = 2..1000</a>
%e A320203 a(2) = 3: {ab}, {ba}, {a,b}.
%e A320203 a(3) = 12: {aab}, {aba}, {abb}, {baa}, {bab}, {bba}, {a,ab}, {a,ba}, {a,bb}, {aa,b}, {ab,b}, {b,ba}.
%e A320203 a(4) = 38: {aaab}, {aaba}, {aabb}, {abaa}, {abab}, {abba}, {abbb}, {baaa}, {baab}, {baba}, {babb}, {bbaa}, {bbab}, {bbba}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {ba,bb}, {a,aa,b}, {a,ab,b}, {a,b,ba}, {a,b,bb}.
%p A320203 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A320203       add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
%p A320203     end:
%p A320203 a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(2):
%p A320203 seq(a(n), n=2..35);
%Y A320203 Column k=2 of A319501.
%K A320203 nonn
%O A320203 2,1
%A A320203 _Alois P. Heinz_, Oct 07 2018