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.

A238085 Expansion of e.g.f.: -LambertW(-sinh(x)).

Original entry on oeis.org

0, 1, 2, 10, 72, 716, 9088, 140344, 2554240, 53540368, 1270296064, 33653698464, 984753299456, 31542901202112, 1097763264864256, 41247391653500800, 1664188908529156096, 71759140177774010624, 3293251384307726942208, 160272893566770148403712
Offset: 0

Views

Author

Vaclav Kotesovec, Feb 17 2014

Keywords

Crossrefs

Programs

  • Mathematica
    CoefficientList[Series[-LambertW[-Sinh[x]],{x,0,20}],x]*Range[0,20]!
  • PARI
    x='x+('x^30); concat([0], Vec(serlaplace(-lambertw(-sinh(x))))) \\ G. C. Greubel, Feb 19 2018

Formula

a(n) ~ (exp(-2)+1)^(1/4) * n^(n-1) / ((log(sqrt(1+exp(-2)) + exp(-1)) )^(n-1/2) * exp(n-1/2)).

A277475 E.g.f.: -sin(x)*LambertW(-x).

Original entry on oeis.org

0, 0, 2, 6, 32, 300, 3576, 52234, 906688, 18229176, 416505760, 10657541422, 301871501568, 9375794555556, 316817746172032, 11570642333807730, 454152692297009152, 19064517871187079408, 852278820775206658560, 40424330665968520135382, 2027524052626732381306880
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 17 2016

Keywords

Crossrefs

Programs

  • Mathematica
    CoefficientList[Series[-Sin[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
    Table[Sum[Binomial[n, k] * Sin[Pi*(n-k)/2] * k^(k-1), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)
  • PARI
    x='x+O('x^50); concat([0,0], Vec(serlaplace(-sin(x)*lambertw(-x)) )) \\ G. C. Greubel, Nov 07 2017

Formula

a(n) ~ sin(exp(-1)) * n^(n-1).

A277478 E.g.f.: -cosh(x)*LambertW(-x).

Original entry on oeis.org

0, 1, 2, 12, 76, 720, 8766, 131096, 2319416, 47361600, 1096018330, 28344108672, 810053677764, 25352185339520, 862335856149782, 31674845755622400, 1249527587684729584, 52687201308036059136, 2364751154207006978994, 112562199977955164819456
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 17 2016

Keywords

Crossrefs

Programs

  • Mathematica
    CoefficientList[Series[-Cosh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
    Table[Sum[(1 + (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]
  • PARI
    x='x+O('x^50); concat([0], Vec(serlaplace(-cosh(x)*lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017

Formula

a(n) = Sum_{k=1..n} (1 + (-1)^(n-k)) * binomial(n,k) * k^(k-1)/2.
a(n) ~ cosh(exp(-1)) * n^(n-1).
Showing 1-3 of 3 results.