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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

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

EXAMPLE

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}.

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);

CROSSREFS

Column k=2 of A319501.

Sequence in context: A319077 A008907 A048246 * A217093 A278639 A222643

Adjacent sequences:  A320200 A320201 A320202 * A320204 A320205 A320206

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 07 2018

STATUS

approved

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Last modified August 6 16:05 EDT 2020. Contains 336255 sequences. (Running on oeis4.)