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 A339014 #13 Nov 19 2020 18:42:39
%S A339014 1,0,0,2,2,2,42,142,366,3082,18626,86990,596158,4485626,30214498,
%T A339014 224897662,1871664190,15587540042,134045407458,1231183979886,
%U A339014 11725017784574,114812031304986,1170100796863202,12371771640238174,134796972965052350,1514854948728869354
%N A339014 E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2)).
%H A339014 Seiichi Manyama, <a href="/A339014/b339014.txt">Table of n, a(n) for n = 0..563</a>
%F A339014 a(0) = 1; a(n) = 2 * Sum_{k=3..n} binomial(n-1,k-1) * a(n-k).
%F A339014 a(n) = Sum_{k=0..n} binomial(n,k) * A006505(k) * A006505(n-k).
%t A339014 nmax = 25; CoefficientList[Series[Exp[2 (Exp[x] - 1 - x - x^2/2)], {x, 0, nmax}], x] Range[0, nmax]!
%t A339014 a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 25}]
%o A339014 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(2 * (exp(x) - 1 - x - x^2/2)))) \\ _Michel Marcus_, Nov 19 2020
%Y A339014 Cf. A001861, A006505, A194689.
%K A339014 nonn
%O A339014 0,4
%A A339014 _Ilya Gutkovskiy_, Nov 19 2020