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.

A213132 Polylogarithm li(-n,-1/9) multiplied by (10^(n+1))/9.

Original entry on oeis.org

1, -1, -8, -46, 64, 7280, 118720, 406160, -35578880, -1156775680, -12796467200, 444964083200, 27457634713600, 594958346547200, -9096689344716800, -1258068242084608000, -45330583283597312000, 24150498582339584000, 95678058298287259648000, 5379182782796767182848000
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=9.

Examples

			polylog(-5, -1/9)*10^6/9 = 7280.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213131
Cf. A213133 to A213157

Programs

  • Maple
    seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*9^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013
  • Mathematica
    Table[If[n == 0, 1, PolyLog[-n, -1/9] 10^(n+1)/9], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)
  • PARI
    /* See A212846; run limnpq(nmax, 1, 9) */
  • PARI
    x='x+O('x^66); Vec(serlaplace( 10/(9+exp(10*x)) )) \\ Joerg Arndt, Apr 21 2013
  • PARI
    a(n) = sum(k=0, n, k!*(-1)^k*10^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=9.
E.g.f.: 10/(9+exp(10*x)). [Joerg Arndt, Apr 21 2013]
a(n) = Sum_{k=0..n} k! * (-1)^k * 10^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022

A213134 Polylogarithm li(-n,-2/5) multiplied by (7^(n+1))/5.

Original entry on oeis.org

1, -2, -6, 22, 426, 598, -54006, -568778, 8381226, 277762198, -123822006, -141432141578, -1958226061974, 70457642899798, 2812274227385994, -17169209695778378, -3417280244608089174, -48220222006064346602
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=2,q=5.

Examples

			polylog(-5,-2/5)*7^6/5 = 598.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213133.
Cf. A213135 to A213157.

Programs

  • Mathematica
    f[n_] := PolyLog[-n, -2/5] 7^(n + 1)/5; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)
  • PARI
    \\ in A212846; run limnpq(nmax, 2, 5)
  • PARI
    a(n) = sum(k=0, n, k!*(-2)^k*7^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=2,q=5.
a(n) = Sum_{k=0..n} k! * (-2)^k * 7^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 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.
Showing 1-3 of 3 results.

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