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

Author

Leroy Quet, Sep 01 2005

Keywords

• nonn
• frac

Comments

Conjecture: a(n)/A112291(n) tends to 2 as n tends to infinity. - Vaclav Kotesovec, Jun 02 2022

Examples

			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,
		

Links

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

Crossrefs

Cf. A112291.

Programs

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 *)

Extensions

Extended by Emeric Deutsch and Ray Chandler, Sep 02 2005