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.

Previous Showing 31-36 of 36 results.

A213153 Polylogarithm li(-n,-8/9) multiplied by (17^(n+1))/9.

Original entry on oeis.org

1, -8, -8, 1144, 4600, -650888, -5610248, 782393464, 11721120760, -1604217628808, -37345505230088, 4993399538404984, 168423884058659320, -21890458098275195528, -1020495088251266584328
Offset: 0

Views

Author

Stanislav Sykora, Jun 06 2012

Keywords

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=8,q=9.

Examples

			polylog(-5,-8/9)*17^6/9 = -650888.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213152.
Cf. A213154 to A213157.

Programs

  • Mathematica
    p = 8; q = 9; f[n_] := PolyLog[-n, -p/q] (p + q)^(n + 1)/q; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)
  • PARI
    in A212846; run limnpq(nmax, 8, 9)

Formula

See formula in A212846, setting p=8,q=9.

A213154 Polylogarithm li(-n,-9/10) multiplied by (19^(n+1))/10.

Original entry on oeis.org

1, -9, -9, 1611, 6471, -1148589, -9872289, 1732196331, 25810293591, -4461906502269, -102948316013169, 17472999720383451, 581452715402943111, -96525920129033025549, -4413961128482041139649
Offset: 0

Views

Author

Stanislav Sykora, Jun 06 2012

Keywords

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=9,q=10.

Examples

			polylog(-5,-9/10)*19^6/10 = -1148589.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213153.
Cf. A213155 to A213157.

Programs

  • Mathematica
    p = 9; q = 10; f[n_] := PolyLog[-n, -p/q] (p + q)^(n + 1)/q; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)
  • PARI
    in A212846; run limnpq(nmax, 9, 10)

Formula

See formula in A212846, setting p=9,q=10.

A213155 Polylogarithm li(-n,-1/100) multiplied by (101^(n+1))/100.

Original entry on oeis.org

1, -1, -99, -9601, -891099, -74657401, -4598985699, 83304101999, 105616323905301, 26458809087970199, 4788219040686298701, 620396956870561833599, 15434896384804497301701, -25743663357271554846442201
Offset: 0

Views

Author

Stanislav Sykora, Jun 06 2012

Keywords

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=100.

Examples

			polylog(-5,-1/100)*101^6/100 = -74657401.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213154.
Cf. A213156, A213157.

Programs

  • Mathematica
    f[n_] := PolyLog[-n, -1/100] (101^(n + 1))/100; f[0] = 1; Array[f, 14, 0] (* Robert G. Wilson v, Dec 25 2015 *)
  • PARI
    in A212846; run limnpq(nmax, 1, 100)

Formula

See formula in A212846, setting p=1,q=100.

A213156 Polylogarithm li(-n,-1/1000) multiplied by (1001^(n+1))/1000.

Original entry on oeis.org

1, -1, -999, -996001, -989010999, -974065974001, -943301698056999, -881188585190880001, -757277396614707246999, -512519922101780607498001, -34386117044101144161012999
Offset: 0

Views

Author

Stanislav Sykora, Jun 06 2012

Keywords

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=1000.

Examples

			polylog(-5,-1/1000)*1001^6/1000 = -974065974001.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127-A213155, A213157.

Programs

  • PARI
    in A212846; run limnpq(nmax, 1, 1000)

Formula

See formula in A212846, setting p=1, q=1000.

A354062 a(n) = Li(-2^n, 1/3), where Li(n, z) is the polylogarithm function.

Original entry on oeis.org

15, 17295, 4229255279355, 11811493418737804581195936694907475
Offset: 2

Views

Author

Amiram Eldar, May 16 2022

Keywords

Comments

The next term, a(6) = 2.808...*10^86, is too large to include in the data section.
a(n) is an integer for all n >= 2 (Aloff, 2022).
Conjecture: for k >= 0, a(n) is divisible by 2^2^k+1 = A000215(k) for all n >= 2^max{k,1}. - Jianing Song, May 17 2022

Links

Crossrefs

Cf. A210246, A212846, A212847, A213127.

Programs

  • Mathematica
    a[n_] := PolyLog[-2^n, 1/3]; Array[a, 5, 2]
  • PARI
    a(n) = polylog(-2^n, 1/3); \\ Michel Marcus, May 16 2022

Formula

a(n) = Sum_{k>=1} k^2^n/3^k. - Jianing Song, May 17 2022

A355373 a(n) = Sum_{k=0..n} k! * (-1)^k * n^(n-k) * Stirling2(n,k).

Original entry on oeis.org

1, -1, 0, 3, 40, 455, 2016, -177373, -11564160, -497664081, -12796467200, 536297904659, 132025634657280, 14907422733429239, 1181852660381503488, 34684559693802943875, -11771644802057621110784, -3553614228958108389522721, -656899368126170250221715456
Offset: 0

Views

Author

Seiichi Manyama, Jun 30 2022

Keywords

Crossrefs

Cf. A212846, A213127, A213128, A213129, A213130, A213131, A213132, A213133.
Cf. A318183, A352074.

Programs

  • Mathematica
    a[n_] := Sum[k! * (-1)^k * n^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *)
  • PARI
    a(n) = sum(k=0, n, k!*(-1)^k*n^(n-k)*stirling(n, k, 2));

Formula

a(n) = n! * [x^n] n/(n - 1 + exp(n*x)) for n > 0.
Previous Showing 31-36 of 36 results.

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