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 A352914 #41 Dec 28 2022 05:42:49
%S A352914 1,2,10,74,676,7592,97024,1416200,23015248,412777952,8090869984,
%T A352914 171435904928,3908548404160,95264270043776,2470715015425024,
%U A352914 67913132377486208,1971038886452490496,60212661838223997440,1930529043247940342272,64801071784954698480128
%N A352914 Expansion of e.g.f. exp(Sum_{k>=1} prime(k)*x^k).
%F A352914 a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A033286(k) * a(n-k)/(n-k)!.
%p A352914 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
%p A352914 ithprime(j)*j*binomial(n, j)*j!, j=1..n)/n)
%p A352914 end:
%p A352914 seq(a(n), n=0..20); # _Alois P. Heinz_, Apr 28 2022
%t A352914 a[0] = 1; a[n_] := a[n] = (n-1)! Sum[k Prime[k] a[n-k]/(n-k)!, {k, 1, n}];
%t A352914 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Dec 28 2022 *)
%o A352914 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, prime(k)*x^k))))
%o A352914 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*prime(k)*a(n-k)/(n-k)!));
%Y A352914 Cf. A000040, A007446, A033286, A353162, A353166.
%K A352914 nonn
%O A352914 0,2
%A A352914 _Seiichi Manyama_, Apr 28 2022