A112289 -id:A112289 - cp's OEIS frontend

A112288 Numerator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.

1, 2, 11, 47, 4999, 4589867, 1802849, 80995354865, 10388318700333839827, 129530631982136545940863, 460116344514106299899953231, 1272711183040784735474188752842879054737

Offset: 1

Leroy Quet, Sep 01 2005

4 consecutive values are primes: 2, 11, 47, 4999. - Jonathan Vos Post, Sep 08 2005

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

Cf. A112289.

a := n -> numer(add(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[Numerator[f[n]], {n, 15}] (* Ray Chandler, Sep 02 2005 *)

a(n) = numerator(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

A354479 a(n) is the denominator of Sum_{k=1..n} 1 / Stirling1(n,k).

Original entry on oeis.org

1, 1, 6, 33, 4200, 4192200, 5115600, 545250747888, 10086416728304192640, 126556188275836361347200, 451535899566923284351392000, 250606479905655959999200124455664175360, 1493469115548888160803495265626573200563200, 47083781674990641531154175811928872812783834939059200

Offset: 1

Ilya Gutkovskiy, Jun 02 2022

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

Cf. A008275, A046826, A112289, A112291, A354478 (numerators).

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

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

cp's OEIS Frontend

A112288 Numerator 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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