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 A365107 #4 Aug 24 2023 10:34:07
%S A365107 1,0,1,1,18,101,1550,22492,424536,10283064,272319552,8959493401,
%T A365107 328044534576,13799304374077,657306569855728,34694458662034731,
%U A365107 2048559070407831424,132868259271772801185,9463476338179250300352,736376651361995115417850,62178423492630241909006224,5689134205956573233701281462
%N A365107 Sum_{n>=0} a(n) * x^n / n!^2 = exp( Sum_{n>=1} x^prime(n) / prime(n)!^2 ).
%F A365107 a(0) = 1; a(n) = (1/n) * Sum_{p <= n, p prime} binomial(n,p)^2 * p * a(n-p).
%t A365107 nmax = 21; CoefficientList[Series[Exp[Sum[x^Prime[k]/Prime[k]!^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A365107 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, Prime[k]]^2 Prime[k] a[n - Prime[k]], {k, 1, PrimePi[n]}]; Table[a[n], {n, 0, 21}]
%Y A365107 Cf. A023998, A190476.
%K A365107 nonn
%O A365107 0,5
%A A365107 _Ilya Gutkovskiy_, Aug 21 2023