A112290 Numerator of sum{k=1 to n} 1/S(n,k), where S(n,k) is a Stirling number of the second kind.

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

Vaclav Kotesovec, Table of n, a(n) for n = 1..49

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

Adjacent sequences: A112287 A112288 A112289 * A112291 A112292 A112293

Keyword

nonn,frac

Author

Leroy Quet, Sep 01 2005

Extensions

Extended by Emeric Deutsch and Ray Chandler, Sep 02 2005

Status

approved