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A112290
Numerator of sum{k=1 to n} 1/S(n,k), where S(n,k) is a Stirling number of the second kind.
3
1, 2, 7, 97, 331, 77089, 562609, 19352053463, 6781959158383, 4060488497950626661, 2877117441205884350399, 7936150834464388482084637351, 21924183158935156780838459
OFFSET
1,2
COMMENTS
Conjecture: a(n)/A112291(n) tends to 2 as n tends to infinity. - Vaclav Kotesovec, Jun 02 2022
LINKS
EXAMPLE
a(4) = 97, the numerator of 1/1 + 1/7 + 1/6 + 1 = 97/42.
The first few fractions are: 1, 2, 7/3, 97/42, 331/150, 77089/36270, 562609/270900,
MAPLE
with(combinat): a:=n->numer(sum(1/stirling2(n, k), k=1..n)): seq(a(n), n=1..15); # Emeric Deutsch, Sep 02 2005
MATHEMATICA
f[n_] := Sum[1/StirlingS2[n, k], {k, n}]; Table[Numerator[f[n]], {n, 15}] (* Ray Chandler, Sep 02 2005 *)
CROSSREFS
Cf. A112291.
Sequence in context: A304722 A056161 A076740 * A072059 A308961 A240696
KEYWORD
nonn,frac
AUTHOR
Leroy Quet, Sep 01 2005
EXTENSIONS
Extended by Emeric Deutsch and Ray Chandler, Sep 02 2005
STATUS
approved