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 1-4 of 4 results.

A362244 Expansion of e.g.f. 1/(1 - x * exp(-x * (exp(-x) - 1))).

Original entry on oeis.org

1, 1, 2, 12, 60, 440, 3810, 37212, 430696, 5482080, 78252390, 1227201140, 20955546348, 388492703040, 7745445183658, 165550236166980, 3773990094033360, 91401848785134272, 2344168680183033678, 63455096201600595060, 1808160553359068792020
Offset: 0

Views

Author

Seiichi Manyama, Apr 12 2023

Keywords

Crossrefs

Cf. A362245, A362246, A362247.
Cf. A362237.

Programs

  • Mathematica
    With[{nn=20},CoefficientList[Series[1/(1-x Exp[-x(Exp[-x]-1)]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 27 2024 *)
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(-x*(exp(-x)-1)))))

Formula

a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! ).

A362247 Expansion of e.g.f. exp(x * exp(x * (exp(x) - 1))).

Original entry on oeis.org

1, 1, 1, 7, 37, 201, 1531, 12433, 112729, 1158769, 12920311, 157007841, 2063354437, 29052921769, 436908104179, 6981843029281, 118083965782321, 2106973566128865, 39538081855597807, 778216030845226561, 16027517577057849181, 344635879922587951321
Offset: 0

Views

Author

Seiichi Manyama, Apr 12 2023

Keywords

Crossrefs

Cf. A362244, A362245, A362246.
Cf. A000258, A202152.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(x*(exp(x)-1)))))

Formula

a(n) = n! * Sum_{i=0..n} ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! )/i!.

A362246 Expansion of e.g.f. exp(x * exp(-x * (exp(-x) - 1))).

Original entry on oeis.org

1, 1, 1, 7, 13, 81, 391, 1093, 18537, 577, 1013131, -54339, 39429853, 424162753, -4130181873, 137131757701, -1733851435439, 29708533549953, -337960798083053, 3890007865959661, -11844138798049659, -662440203084569279, 30135319297423429783
Offset: 0

Views

Author

Seiichi Manyama, Apr 12 2023

Keywords

Crossrefs

Cf. A362244, A362245, A362247.
Cf. A347726.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-x*(exp(-x)-1)))))

Formula

a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! )/i!.

A362274 Expansion of e.g.f. 1/(1-x*exp(x*exp(x))).

Original entry on oeis.org

1, 1, 4, 27, 232, 2465, 31416, 467173, 7940080, 151824177, 3225664720, 75386002901, 1921987809336, 53085088574713, 1578989028324904, 50320957240554645, 1710595789688360416, 61783832256587799137, 2362794061464082513440, 95380148553556615501717
Offset: 0

Views

Author

Seiichi Manyama, Apr 13 2023

Keywords

Links

Crossrefs

Cf. A000949, A362273, A362275.
Cf. A362245.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x*exp(x)))))

Formula

a(n) = n! * Sum_{i=0..n} Sum_{j=0..n-i} i^j * j^(n-i-j) / (j! * (n-i-j)!).
Showing 1-4 of 4 results.

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

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