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 A365106 #4 Aug 24 2023 10:33:59
%S A365106 1,2,11,107,1577,32201,860460,28921567,1187475909,58232016701,
%T A365106 3350187053856,222857979706305,16935374386652282,1455271176236200143,
%U A365106 140181486948923188907,15023106134895469195114,1779460642743292348315607,231607462899834684300774917,32954119475274480307491604062,5102159139278049158548905019487
%N A365106 Sum_{n>=0} a(n) * x^n / n!^2 = exp( Sum_{n>=1} prime(n) * x^n / n!^2 ).
%F A365106 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * prime(k) * a(n-k).
%t A365106 nmax = 19; CoefficientList[Series[Exp[Sum[Prime[k] x^k/k!^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A365106 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k Prime[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%Y A365106 Cf. A007446, A023998.
%K A365106 nonn
%O A365106 0,2
%A A365106 _Ilya Gutkovskiy_, Aug 21 2023