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.

A367080 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2).

Original entry on oeis.org

1, 1, 5, 50, 766, 15914, 418548, 13337624, 499600848, 21516318360, 1047593782440, 56903921842272, 3411723783002016, 223803339516120480, 15944855840879771232, 1226078375934824887680, 101209861891840507123200, 8926972851724904613537792
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Cf. A138013, A367152.
Cf. A367078, A367153.

Programs

  • Mathematica
    Table[(2*n)! * Sum[Abs[StirlingS1[n,k]]/(2*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
  • PARI
    a(n) = (2*n)!*sum(k=0, n, abs(stirling(n, k, 1))/(2*n-k+1)!);

Formula

a(n) = (2*n)! * Sum_{k=0..n} |Stirling1(n,k)|/(2*n-k+1)!.
a(n) ~ (-2 - LambertW(-1, -2*exp(-3)))^(n+1) * (-LambertW(-1, -2*exp(-3)))^n * n^(n-1) / (sqrt(-2 - 2*LambertW(-1, -2*exp(-3))) * exp(n)). - Vaclav Kotesovec, Nov 07 2023

A367153 E.g.f. satisfies A(x) = 2 - exp(-x*A(x)^2).

Original entry on oeis.org

1, 1, 3, 13, 55, -59, -8869, -230019, -4735569, -81845819, -925266221, 11304277117, 1342388191079, 64570153427781, 2378028350945547, 68237841920780221, 1044508709568828511, -45901762542718407035, -5887687395597254917885, -396339747040666473203907
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Cf. A097718, A367154.
Cf. A367078, A367080.

Programs

  • PARI
    a(n) = (2*n)!*sum(k=0, n, (-1)^(n-k)*stirling(n, k, 2)/(2*n-k+1)!);

Formula

a(n) = (2*n)! * Sum_{k=0..n} (-1)^(n-k) * Stirling2(n,k)/(2*n-k+1)!.

A367079 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).

Original entry on oeis.org

1, 1, 5, 47, 654, 12084, 278682, 7708056, 248678784, 9168447600, 380274659760, 17524760349216, 888364833282000, 49125202031205936, 2942774373267939168, 189829708902667840320, 13118899353628035596544, 966975804677206274688000
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Comments

a(131) is negative. - Vaclav Kotesovec, Nov 07 2023

Links

Crossrefs

Cf. A185221, A367078.
Cf. A367152, A367154.

Programs

  • Mathematica
    Table[(3*n)! * Sum[StirlingS1[n,k]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
  • PARI
    a(n) = (3*n)!*sum(k=0, n, stirling(n, k, 1)/(3*n-k+1)!);

Formula

a(n) = (3*n)! * Sum_{k=0..n} Stirling1(n,k)/(3*n-k+1)!.
Showing 1-3 of 3 results.

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

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