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 A353163 #13 Apr 28 2022 09:50:49
%S A353163 1,0,2,3,12,65,210,1477,7560,45864,338310,2176031,17657640,139280869,
%T A353163 1150004856,10572694860,94834041120,931995595457,9384294360168,
%U A353163 96974005210273,1066116104926500,11838081891521760,137785102884102366,1652584041236345933
%N A353163 Expansion of e.g.f. exp(Sum_{p prime} x^p / (p-1)!).
%F A353163 a(0) = 1; a(n) = Sum_{p<=n, p prime} p * binomial(n-1,p-1) * a(n-p).
%o A353163 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, isprime(k)*x^k/(k-1)!))))
%o A353163 (PARI) a(n) = if(n==0, 1, sum(k=1, n, isprime(k)*k*binomial(n-1, k-1)*a(n-k)));
%Y A353163 Cf. A000040, A000248, A190476, A353162.
%K A353163 nonn
%O A353163 0,3
%A A353163 _Seiichi Manyama_, Apr 28 2022