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 A353165 #12 Apr 28 2022 09:51:01
%S A353165 1,0,2,3,24,125,900,7987,72240,817488,9536940,127816931,1830739680,
%T A353165 28597812685,481145656992,8650951895040,166376275228800,
%U A353165 3392537585542577,73342277086465296,1672523286398099407,40158685461798481560,1012415090497566344400
%N A353165 Expansion of e.g.f. 1/(1 - Sum_{p prime} x^p / (p-1)!).
%F A353165 a(0) = 1; a(n) = Sum_{p<=n, p prime} p * binomial(n,p) * a(n-p).
%o A353165 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, isprime(k)*x^k/(k-1)!))))
%o A353165 (PARI) a(n) = if(n==0, 1, sum(k=1, n, isprime(k)*k*binomial(n, k)*a(n-k)));
%Y A353165 Cf. A000040, A006153, A347948, A353163, A353164.
%K A353165 nonn
%O A353165 0,3
%A A353165 _Seiichi Manyama_, Apr 28 2022