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

A367078 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2).

Original entry on oeis.org

1, 1, 3, 14, 82, 514, 2508, -12328, -820752, -22232232, -498433320, -9865850688, -159373484448, -1136343398880, 65056426313760, 4663237803223680, 210535052582008320, 7821007002377349120, 242387957802121971840, 5333182310844833642496
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Cf. A185221, A367079.
Cf. A367080, A367153.

Programs

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

Formula

a(n) = (2*n)! * Sum_{k=0..n} Stirling1(n,k)/(2*n-k+1)!.

A367154 E.g.f. satisfies A(x) = 2 - exp(-x*A(x)^3).

Original entry on oeis.org

1, 1, 5, 46, 611, 10486, 217817, 5232298, 139988039, 4014151966, 116960920469, 3089842957378, 42760230799211, -3590078035238330, -540748879852479439, -53293187072033883494, -4741372656403996001905, -409753919036526362138834
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Cf. A097718, A367153.

Programs

  • PARI
    a(n) = (3*n)!*sum(k=0, n, (-1)^(n-k)*stirling(n, k, 2)/(3*n-k+1)!);

Formula

a(n) = (3*n)! * Sum_{k=0..n} (-1)^(n-k) * Stirling2(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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