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 A355380 #15 Jul 03 2022 04:45:25
%S A355380 1,5,38,355,3879,48050,661163,9961745,162598044,2851150665,
%T A355380 53350521523,1059447004560,22224898346989,490589320542305,
%U A355380 11356591577861398,274886065370874775,6939205217774546339,182273695066097752170,4971724931587003394863,140559648864263508395965
%N A355380 Expansion of e.g.f. exp(exp(3*x) + exp(2*x) - 2).
%H A355380 Seiichi Manyama, <a href="/A355380/b355380.txt">Table of n, a(n) for n = 0..463</a>
%F A355380 a(n) = Sum_{k=0..n} binomial(n,k) * 3^k * 2^(n-k) * Bell(k) * Bell(n-k).
%F A355380 a(0) = 1; a(n) = Sum_{k=1..n} (3^k + 2^k) * binomial(n-1,k-1) * a(n-k). - _Seiichi Manyama_, Jun 30 2022
%F A355380 a(n) ~ exp(exp(3*z) + exp(2*z) - 2 - n) * (n/z)^(n + 1/2) / sqrt(3*(1 + 3*z)*exp(3*z) + 2*(1 + 2*z)*exp(2*z)), where z = LambertW(n)/3 - 1/(2 + 3/LambertW(n) + 9 * n^(1/3) * (1 + LambertW(n)) / (2*LambertW(n)^(4/3))). - _Vaclav Kotesovec_, Jul 03 2022
%t A355380 nmax = 20; CoefficientList[Series[Exp[Exp[3*x] + Exp[2*x] - 2], {x, 0, nmax}], x] * Range[0, nmax]!
%t A355380 Table[Sum[Binomial[n,k] * 3^k * 2^(n-k) * BellB[k] * BellB[n-k], {k, 0, n}], {n, 0, 20}]
%o A355380 (PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(exp(3*x) + exp(2*x) - 2))) \\ _Michel Marcus_, Jun 30 2022
%Y A355380 Cf. A143405, A355291, A355381.
%K A355380 nonn
%O A355380 0,2
%A A355380 _Vaclav Kotesovec_, Jun 30 2022