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%I #21 Mar 24 2024 08:14:09
%S 1,2,5,23,101,511,3300,20499,147249,1158047,9284124,82250155,
%T 762408746,7406758725,75928931645,815389826454,9127145085135,
%U 106002459387831,1287304713397098,16132127163478581,209381715443456410,2814011969429674997,38957100435462040565
%N Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^prime(k).
%C "EGJ" (unordered, element, labeled) transform of primes.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%t nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000040, A007837, A032315, A032316, A061152.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 24 2024