A362237 -id:A362237 - 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)! ).

A362238 Expansion of e.g.f.: 1/(1 - x*(1+x)^x).

Original entry on oeis.org

1, 1, 2, 12, 60, 460, 3900, 39438, 456288, 5896224, 85230000, 1349017560, 23353941600, 437432418696, 8828284404576, 190867622500800, 4401749312069760, 107859517575659520, 2798352667710645120, 76636669899079699776, 2209235394261812751360

Offset: 0

Seiichi Manyama, Apr 12 2023

nonn

Cf. A202152, A362237.

Cf. A002478, A099234, A099235.

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

a(n) = n! * Sum_{i=0..n} Sum_{j=0..n-i} i^j * Stirling1(n-i-j,j)/(n-i-j)!.

cp's OEIS Frontend

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

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