A362238 -id:A362238 - cp's OEIS frontend

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

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

A362237 Expansion of e.g.f.: 1/(1 - x/(1-x)^x).

Original entry on oeis.org

1, 1, 2, 12, 84, 700, 7140, 84798, 1148448, 17508384, 296577360, 5525645400, 112311096480, 2473005981576, 58642262698656, 1489908226161600, 40377279733096320, 1162635170476462080, 35446505436393782400, 1140734265246337985856, 38643098112640927503360

Offset: 0

Seiichi Manyama, Apr 12 2023

nonn

Cf. A347726, A362238.

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

a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling1(n-i-j,j)/(n-i-j)! ).

cp's OEIS Frontend

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

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