A345750 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k).
1, 1, 2, 9, 49, 310, 2521, 25557, 290550, 3555041, 48104901, 741103946, 12825399313, 240202011881, 4747281446090, 98808864563065, 2194031697420057, 52582450760730398, 1357237338948268649
Offset: 0
Keywords
Links
- N. J. A. Sloane, Transforms
- Eric Weisstein's World of Mathematics, Stirling Transform
Programs
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Mathematica
max = 18; Range[0, max]! * CoefficientList[Series[Product[(1 + (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k)))) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, -sumdiv(k, d, (-1)^d)*(exp(x)-1)^k/k))))
Comments