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.

A375604 Expansion of e.g.f. 1 / (exp(-x^2) - x).

Original entry on oeis.org

1, 1, 4, 18, 108, 840, 7680, 82320, 1009680, 13910400, 213071040, 3589850880, 65975152320, 1313624632320, 28166959941120, 647099547494400, 15857424488505600, 412878579034521600, 11382450106662835200, 331230511848421785600, 10146149192841050188800
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2024

Keywords

Crossrefs

Cf. A072597, A375607.
Cf. A375394, A375608.

Programs

  • Mathematica
    With[{nn=20},CoefficientList[Series[1/(Exp[-x^2]-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 01 2025 *)
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^2)-x)))
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k+1)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^k/k!.
a(n) ~ sqrt(Pi) * 2^(n/2 + 1) * n^(n + 1/2) / ((1 + LambertW(2)) * exp(n) * LambertW(2)^((n+1)/2)). - Vaclav Kotesovec, Aug 21 2024

A375628 Expansion of e.g.f. exp(2*x^3) / (1 - x * exp(x^3)).

Original entry on oeis.org

1, 1, 2, 18, 96, 600, 5760, 57960, 645120, 8285760, 117936000, 1842825600, 31374604800, 578334556800, 11493004723200, 244720360684800, 5555523785011200, 134002274473267200, 3422904611167641600, 92290617116425728000, 2619214995575033856000
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2024

Keywords

Crossrefs

Cf. A368265, A375627.
Cf. A358065, A375607.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^3)/(1-x*exp(x^3))))
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k+2)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+2)^k/k!.

A375634 Expansion of e.g.f. exp(x^3) / (1 - x * exp(x^3/6)).

Original entry on oeis.org

1, 1, 2, 12, 52, 280, 2160, 16870, 150080, 1557360, 17491600, 215908000, 2923905600, 42734091400, 672515043200, 11347480544400, 204142655516800, 3902009862150400, 78976503077472000, 1687212801048174400, 37941749192547200000
Offset: 0

Views

Author

Seiichi Manyama, Aug 22 2024

Keywords

Crossrefs

Cf. A358265, A375607, A375633.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x*exp(x^3/6))))
  • PARI
    a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k/k!.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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