A112288 -id:A112288 - cp's OEIS frontend

A112289 Denominator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.

1, 1, 6, 33, 4200, 4192200, 1705200, 77892963984, 10086416728304192640, 126556188275836361347200, 451535899566923284351392000, 1253032399528279799996000622278320876800

Offset: 1

Leroy Quet, Sep 01 2005

			a(4) = 33, the denominator of 1/6 + 1/11 + 1/6 + 1 = 47/33.
The first few fractions are: 1, 2, 11/6, 47/33, 4999/4200.

Cf. A112288.

with(combinat): a:=n->denom(sum(1/abs(stirling1(n,k)),k=1..n)): seq(a(n),n=1..14); # Emeric Deutsch, Sep 02 2005

f[n_] := Sum[1/Abs[StirlingS1[n, k]], {k, n}]; Table[Denominator[f[n]], {n, 15}] (* Ray Chandler, Sep 02 2005 *)

a(n) = denominator(sum(k=1, n, 1/abs(stirling(n,k,1)))); \\ Michel Marcus, Aug 17 2019

Extended by Emeric Deutsch and Ray Chandler, Sep 02 2005

A354478 a(n) is the numerator of Sum_{k=1..n} 1 / Stirling1(n,k).

Original entry on oeis.org

1, 0, 7, 25, 3991, 3923773, 4901627, 527165212865, 9823031039961293027, 123877274974851473572937, 443645907754951021537851199, 246932542361393897304051461727006396307, 1474846779473982897350113519971401527250089, 46578509609937575127608478711343978511593638945099881

Offset: 1

Ilya Gutkovskiy, Jun 02 2022

Conjecture: a(n)/A354479(n) tends to 1 as n tends to infinity. For comparison: A112290(n)/A112291(n) tends to 2 as n tends to infinity. - Vaclav Kotesovec, Jun 02 2022

			1, 0, 7/6, 25/33, 3991/4200, 3923773/4192200, 4901627/5115600, 527165212865/545250747888, ...

Cf. A008275, A046825, A112288, A112290, A354479 (denominators).

Table[Sum[1/StirlingS1[n, k], {k, 1, n}], {n, 1, 14}] // Numerator

a(n) = numerator(sum(k=1, n, 1/stirling(n, k, 1))); \\ Michel Marcus, Jun 02 2022

cp's OEIS Frontend

A112289 Denominator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.

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