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E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k!).
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%I #13 Jun 26 2021 08:58:39

%S 1,1,2,8,34,137,614,3754,25449,82747,-1523792,-34833005,-335209288,

%T 194665837,59685834069,715582325511,-10186972407657,-584687267399246,

%U -10975484551366964,8845584310341044,8145484883568515927,330326712925212377392,7816903733527799885488

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

%C Stirling transform of A298906.

%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} (-1)^(k+1) * (exp((exp(x) - 1)^k) - 1)/k ).

%F a(n) = Sum_{k=0..n} Stirling2(n,k) * A298906(k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k!))))

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (-1)^(k+1)*(exp((exp(x)-1)^k)-1)/k))))

%Y Cf. A048993, A298906, A345756, A345758.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jun 26 2021