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.

A213129 Polylogarithm li(-n,-1/6) multiplied by (7^(n+1))/6.

Original entry on oeis.org

1, -1, -5, -13, 115, 2099, 11395, -177373, -5116685, -40481581, 948973795, 36701972867, 375364322515, -12090607539661, -580544884927805, -7188739235243293, 301374306966657715, 17150539711123411859, 246564346727945106595, -12988846468460187345853
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=6.

Examples

			polylog(-5,-1/6)*7^6/6 = 2099.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127, A213128.
Cf. A213130 through A213157

Programs

  • Maple
    seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*6^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013
  • Mathematica
    Table[If[n == 0, 1, PolyLog[-n, -1/6] 7^(n+1)/6], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)
  • PARI
    /* See A212846; run limnpq(nmax,1,6) */
  • PARI
    x='x+O('x^66); Vec(serlaplace( 7/(6+exp(7*x)) )) \\ Joerg Arndt, Apr 21 2013
  • PARI
    a(n) = sum(k=0, n, k!*(-1)^k*7^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=6.
E.g.f.: 7/(6+exp(7*x)). [Joerg Arndt, Apr 21 2013]
a(n) = Sum_{k=0..n} k! * (-1)^k * 7^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022

A213131 Polylogarithm li(-n,-1/8) multiplied by (9^(n+1))/8.

Original entry on oeis.org

1, -1, -7, -33, 105, 5199, 64953, -46593, -21769335, -497664081, -1941272487, 256114020447, 9566995408425, 99966666676239, -6245895772363527, -366865939437422913, -6924777575908002615, 259022993102904450159, 24387711970312991335833, 716398360186298080983327
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=8.

Examples

			polylog(-5,-1/8)*9^6/8 = 5199.

Links

Crossrefs

Cf. A212846, A210246, A212847, A213127 to A213130
Cf. A213132 to A213157

Programs

  • Maple
    seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*8^k, k=0..n),n=0..17); # Peter Luschny, Apr 21 2013
  • Mathematica
    Table[If[n == 0, 1, PolyLog[-n, -1/8] 9^(n+1)/8], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)
  • PARI
    /* See A212846; run limnpq(nmax, 1, 8) */
  • PARI
    x='x+O('x^66); Vec(serlaplace( 9/(8+exp(9*x)) )) \\ Joerg Arndt, Apr 21 2013
  • PARI
    a(n) = sum(k=0, n, k!*(-1)^k*9^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022

Formula

See formula in A212846, setting p=1,q=8.
E.g.f.: 9/(8+exp(9*x)). [Joerg Arndt, Apr 21 2013]
a(n) = Sum_{k=0..n} k! * (-1)^k * 9^(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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