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.

3, 12, 38, 110, 302, 806, 2109, 5450, 13917, 35224, 88464, 220608, 546734, 1347290, 3302716, 8057268, 19568800, 47329156, 114025658, 273709580, 654765164, 1561257760, 3711372761, 8797021430, 20794198251, 49024480496, 115292809466, 270495295124, 633186396954

Offset: 2

Author

Alois P. Heinz, Oct 07 2018

Keywords

• nonn

Examples

			a(2) = 3: {ab}, {ba}, {a,b}.
a(3) = 12: {aab}, {aba}, {abb}, {baa}, {bab}, {bba}, {a,ab}, {a,ba}, {a,bb}, {aa,b}, {ab,b}, {b,ba}.
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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000

Crossrefs

Column k=2 of A319501.

Programs

Maple

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(2):
seq(a(n), n=2..35);