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 A307772 #7 Feb 16 2025 08:33:55
%S A307772 2,1,0,-2,14,-100,792,-6984,68112,-728924,8498662,-107269546,
%T A307772 1457660932,-21221947564,329615120330,-5440973779098,95131744001392,
%U A307772 -1756450890029772,34152285999547328,-697588907138104978,14934641645024407092,-334433142861340604942,7818455679081107296154
%N A307772 Expansion of e.g.f. Sum_{k>=1} prime(k)*log(1 + x)^k/k!.
%C A307772 Inverse Stirling transform of primes.
%H A307772 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F A307772 a(n) = Sum_{k=1..n} Stirling1(n,k)*prime(k).
%t A307772 nmax = 23; Rest[CoefficientList[Series[Sum[Prime[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
%t A307772 Table[Sum[StirlingS1[n, k] Prime[k], {k, 1, n}], {n, 1, 23}]
%Y A307772 Cf. A000040, A085507, A307771, A307773.
%K A307772 sign
%O A307772 1,1
%A A307772 _Ilya Gutkovskiy_, Apr 27 2019