A347726 -id:A347726 - cp's OEIS frontend

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

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

Seiichi Manyama, Apr 12 2023

sign

Cf. A362244, A362245, A362247.

Cf. A347726.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(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)! )/i!.

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

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

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