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%I #6 Apr 27 2019 20:35:52
%S 2,1,0,-2,14,-100,792,-6984,68112,-728924,8498662,-107269546,
%T 1457660932,-21221947564,329615120330,-5440973779098,95131744001392,
%U -1756450890029772,34152285999547328,-697588907138104978,14934641645024407092,-334433142861340604942,7818455679081107296154
%N Expansion of e.g.f. Sum_{k>=1} prime(k)*log(1 + x)^k/k!.
%C Inverse Stirling transform of primes.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F a(n) = Sum_{k=1..n} Stirling1(n,k)*prime(k).
%t nmax = 23; Rest[CoefficientList[Series[Sum[Prime[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
%t Table[Sum[StirlingS1[n, k] Prime[k], {k, 1, n}], {n, 1, 23}]
%Y Cf. A000040, A085507, A307771, A307773.
%K sign
%O 1,1
%A _Ilya Gutkovskiy_, Apr 27 2019
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