The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 Aug 10 2021 18:48:26
%S 1,1,3,10,43,206,1044,5909,38371,272314,1995208,14869889,115433344,
%T 965259881,8773348601,84608514095,837220780691,8334354200226,
%U 83498917650084,855936118936073,9180736840445788,104439240481045949,1253608634906635901
%N E.g.f.: Product_{k>=1} (1 + exp(x) * x^k / k!).
%F E.g.f.: exp( Sum_{k>=1} ( Sum_{d|k} (-1)^(d+1) * exp(d*x) / (d * ((k/d)!)^d) ) * x^k ).
%F E.g.f.: Product_{k>=1} (1 + Sum_{j>=k} binomial(j,k) * x^j / j!).
%t nmax = 22; CoefficientList[Series[Product[(1 + Exp[x] x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007837, A265952, A305547, A347005.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 10 2021