A345750
E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k).
Original entry on oeis.org
1, 1, 2, 9, 49, 310, 2521, 25557, 290550, 3555041, 48104901, 741103946, 12825399313, 240202011881, 4747281446090, 98808864563065, 2194031697420057, 52582450760730398, 1357237338948268649
Offset: 0
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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 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k))))
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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))))
A345749
E.g.f.: Product_{k>=1} 1/(1 - (exp(x) - 1)^k)^(1/k).
Original entry on oeis.org
1, 1, 4, 21, 147, 1250, 12633, 147497, 1947676, 28699373, 466994003, 8309274754, 160368858609, 3336869582657, 74468098634660, 1773827462044421, 44905503103938915, 1203843692164105458, 34070243272290551113, 1015056385225183643721
Offset: 0
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max = 19; Range[0, max]! * CoefficientList[Series[Product[1/(1 - (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(exp(x)-1)^k)^(1/k))))
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N,numdiv(k)*(exp(x)-1)^k/k))))
A345752
E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k / k).
Original entry on oeis.org
1, -1, -2, -3, 0, 55, 572, 4865, 40912, 351675, 2978196, 23418373, 148849544, 84185855, -27459134420, -881482705719, -21652972750464, -487503384038525, -10785437160748156, -242968902040697011, -5627949704687484872, -133358411031825299385
Offset: 0
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max = 21; Range[0, max]! * CoefficientList[Series[Product[1 - (Exp[x] - 1)^k/k, {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, 1-(exp(x)-1)^k/k)))
Showing 1-3 of 3 results.
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