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 A347435 #6 Sep 02 2021 21:01:59
%S A347435 1,0,0,0,1,6,22,64,198,1138,10004,83920,617993,4226028,30103686,
%T A347435 251883012,2490287821,26456763078,281404300348,2966101610920,
%U A347435 31877462564554,362624252399566,4437794875670072,57612897938229380,773900876490016325,10599854900351622752
%N A347435 E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6) ).
%C A347435 Exponential transform of A002663.
%F A347435 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002663(k) * a(n-k).
%p A347435 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A347435 a(n-j)*binomial(n-1, j-1)*(2^j-j^3/6-5*j/6-1), j=1..n))
%p A347435 end:
%p A347435 seq(a(n), n=0..25); # _Alois P. Heinz_, Sep 02 2021
%t A347435 nmax = 25; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2 - x^3/6)], {x, 0, nmax}], x] Range[0, nmax]!
%t A347435 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - 1 - k (k^2 + 5)/6) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]
%Y A347435 Cf. A002663, A055882, A057837, A143405, A347432, A347434.
%K A347435 nonn
%O A347435 0,6
%A A347435 _Ilya Gutkovskiy_, Sep 02 2021