A362246 -id:A362246 - cp's OEIS frontend

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

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

Offset: 0

Seiichi Manyama, Apr 12 2023

nonn

Cf. A362245, A362246, A362247.

Cf. A362237.

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 *)

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

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)! ).

A362245 Expansion of e.g.f. 1/(1 - x * exp(x * (exp(x) - 1))).

Original entry on oeis.org

1, 1, 2, 12, 84, 680, 6750, 78372, 1035608, 15402816, 254672730, 4631221100, 91872810612, 1974481960464, 45698618329910, 1133221107064620, 29974735063385520, 842413032202481792, 25067919890384214066, 787394937539847359052, 26034146454319615550540

Offset: 0

Seiichi Manyama, Apr 12 2023

nonn

Cf. A362244, A362246, A362247.

Cf. A362238.

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

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

a(n) ~ n! / ((1 - r + exp(r)*r*(1 + r)) * r^n), where r = 0.60489399462026660841486230237937164068755854932856922096976397761... is the root of the equation exp(r*(exp(r)-1)) = 1/r. - Vaclav Kotesovec, Apr 13 2023

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

Seiichi Manyama, Apr 12 2023

nonn

Cf. A362244, A362245, A362246.

Cf. A000258, A202152.

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

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

cp's OEIS Frontend

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

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A362245 Expansion of e.g.f. 1/(1 - x * exp(x * (exp(x) - 1))).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

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

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula