cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

1, 2, 7, 97, 331, 77089, 562609, 19352053463, 6781959158383, 4060488497950626661, 2877117441205884350399, 7936150834464388482084637351, 21924183158935156780838459
Offset: 1

Views

Author

Leroy Quet, Sep 01 2005

Keywords

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,
		

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

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

Views

Author

Ilya Gutkovskiy, Jun 02 2022

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

  • Mathematica
    Table[Sum[1/StirlingS1[n, k], {k, 1, n}], {n, 1, 14}] // Numerator
  • PARI
    a(n) = numerator(sum(k=1, n, 1/stirling(n, k, 1))); \\ Michel Marcus, Jun 02 2022

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

Views

Author

Ilya Gutkovskiy, Jun 02 2022

Keywords

Examples

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

Crossrefs

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

Programs

  • Mathematica
    Table[Sum[1/StirlingS1[n, k], {k, 1, n}], {n, 1, 14}] // Denominator
  • PARI
    a(n) = denominator(sum(k=1, n, 1/stirling(n, k, 1))); \\ Michel Marcus, Jun 02 2022
Showing 1-3 of 3 results.