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 A347434 #7 Sep 02 2021 21:01:49
%S A347434 1,0,0,1,5,16,52,274,1990,14354,99704,730225,6061013,56151330,
%T A347434 551040830,5597109717,59324775741,664973687438,7891158217876,
%U A347434 98253448977890,1273082291906394,17124091446383666,239333235895599762,3476600533730954761,52394273274018321421
%N A347434 E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2) ).
%C A347434 Exponential transform of A002662.
%F A347434 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002662(k) * a(n-k).
%p A347434 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A347434 a(n-j)*binomial(n-1, j-1)*(2^j-j*(j+1)/2-1), j=1..n))
%p A347434 end:
%p A347434 seq(a(n), n=0..24); # _Alois P. Heinz_, Sep 02 2021
%t A347434 nmax = 24; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2)], {x, 0, nmax}], x] Range[0, nmax]!
%t A347434 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - 1 - k (k + 1)/2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
%Y A347434 Cf. A002662, A006505, A055882, A143405, A347432, A347435.
%K A347434 nonn
%O A347434 0,5
%A A347434 _Ilya Gutkovskiy_, Sep 02 2021