This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345757 #14 Feb 16 2025 08:34:02
%S A345757 1,1,2,8,34,137,614,3754,25449,82747,-1523792,-34833005,-335209288,
%T A345757 194665837,59685834069,715582325511,-10186972407657,-584687267399246,
%U A345757 -10975484551366964,8845584310341044,8145484883568515927,330326712925212377392,7816903733527799885488
%N A345757 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k!).
%C A345757 Stirling transform of A298906.
%H A345757 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A345757 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F A345757 E.g.f.: exp( Sum_{k>=1} (-1)^(k+1) * (exp((exp(x) - 1)^k) - 1)/k ).
%F A345757 a(n) = Sum_{k=0..n} Stirling2(n,k) * A298906(k).
%o A345757 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k!))))
%o A345757 (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 A345757 Cf. A048993, A298906, A345756, A345758.
%K A345757 sign
%O A345757 0,3
%A A345757 _Seiichi Manyama_, Jun 26 2021