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E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k).
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%I #21 Jun 26 2021 08:58:08

%S 1,1,2,9,49,310,2521,25557,290550,3555041,48104901,741103946,

%T 12825399313,240202011881,4747281446090,98808864563065,

%U 2194031697420057,52582450760730398,1357237338948268649

%N E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k).

%C Stirling transform of A168243.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>

%F E.g.f.: exp( Sum_{k>=1} A048272(k) * (exp(x) - 1)^k / k ).

%F a(n) = Sum_{k=0..n} Stirling2(n,k) * A168243(k).

%t 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 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k))))

%o (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))))

%Y Cf. A048272, A048993, A168243, A305550, A305987, A345749, A345751.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 26 2021