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 A355247 #13 Jul 21 2025 03:13:24
%S A355247 1,4,18,90,494,2946,18926,130066,950654,7353794,59954638,513333618,
%T A355247 4601380766,43062556322,419742815726,4252083713874,44680229906622,
%U A355247 486145710591874,5468499473222670,63503107472489266,760281866742088670,9373065303624742498,118858898763010225198
%N A355247 Expansion of e.g.f. exp(2*(exp(x) - 1 + x)).
%H A355247 Vaclav Kotesovec, <a href="/A355247/b355247.txt">Table of n, a(n) for n = 0..550</a>
%F A355247 a(n) ~ n^(n+2) * exp(n/LambertW(n/2) - n - 2) / (4 * sqrt(1 + LambertW(n/2)) * LambertW(n/2)^(n+2)).
%F A355247 a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k+1) * Bell(n-k+1). - _Ilya Gutkovskiy_, Jun 26 2022
%t A355247 nmax = 25; CoefficientList[Series[Exp[2*Exp[x]-2+2*x], {x, 0, nmax}], x] * Range[0, nmax]!
%t A355247 Table[(BellB[n+2, 2] - BellB[n+1, 2])/4, {n, 0, 25}] (* _Vaclav Kotesovec_, Jul 21 2025 *)
%Y A355247 Cf. A000110, A001861, A035009, A194689, A217924, A293024, A339014.
%K A355247 nonn
%O A355247 0,2
%A A355247 _Vaclav Kotesovec_, Jun 25 2022