|
%I #13 Jun 26 2021 08:58:32
%S 1,1,4,20,132,1057,10036,110168,1369395,19009207,291638340,4898978911,
%T 89387432140,1760380295559,37222139393757,841009071062929,
%U 20219172890524757,515336552717107810,13879978696592456136,393920374851547833518,11749388855614114735431
%N E.g.f.: Product_{k>=1} 1/(1 - (exp(x) - 1)^k)^(1/k!).
%C Stirling transform of A209902.
%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} (exp((exp(x) - 1)^k) - 1)/k ).
%F a(n) = Sum_{k=0..n} Stirling2(n,k) * A209902(k).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/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, (exp((exp(x)-1)^k)-1)/k))))
%Y Cf. A048993, A140585, A209902, A345757, A345758.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 26 2021
|
