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 A347948 #5 Sep 20 2021 08:51:36
%S A347948 1,0,1,1,6,21,110,673,4312,34260,280212,2648581,26580840,292468333,
%T A347948 3453838544,43672689816,590203920256,8458029201433,128528293405392,
%U A347948 2059731511022935,34762308371221224,615898019175914166,11432263502365894916,221855824404176472115
%N A347948 E.g.f.: 1 / (1 - Sum_{k>=1} x^prime(k) / prime(k)!).
%F A347948 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A010051(k) * a(n-k).
%t A347948 nmax = 23; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/Prime[k]!, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%t A347948 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Boole[PrimeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%Y A347948 Cf. A000670, A010051, A023360, A190476, A329261, A347949.
%K A347948 nonn
%O A347948 0,5
%A A347948 _Ilya Gutkovskiy_, Sep 20 2021