The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #14 Jun 26 2021 08:58:24
%S 1,-1,-2,-3,0,55,572,4865,40912,351675,2978196,23418373,148849544,
%T 84185855,-27459134420,-881482705719,-21652972750464,-487503384038525,
%U -10785437160748156,-242968902040697011,-5627949704687484872,-133358411031825299385
%N E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k / k).
%C Stirling transform of A292359.
%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 a(n) = Sum_{k=0..n} Stirling2(n,k) * A292359(k).
%t 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 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, 1-(exp(x)-1)^k/k)))
%Y Cf. A048993, A292359, A305986, A305987, A345751.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jun 26 2021