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 A354551 #21 Mar 03 2025 13:08:37
%S A354551 1,1,1,1,5,21,61,211,1401,8065,37241,240021,1997821,13856701,94418325,
%T A354551 874328911,8304303281,69158458881,658339599601,7454839614985,
%U A354551 78224066633781,805961931388741,9828080719704941,124199805022959051,1466207770078872745
%N A354551 Expansion of e.g.f. exp( x * exp(x^3/6) ).
%C A354551 This sequence is different from A143567.
%H A354551 Seiichi Manyama, <a href="/A354551/b354551.txt">Table of n, a(n) for n = 0..523</a>
%F A354551 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * k! * (n - 3*k)!).
%t A354551 With[{nn=30},CoefficientList[Series[Exp[x*Exp[x^3/6]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 03 2025 *)
%o A354551 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)))))
%o A354551 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*k!*(n-3*k)!));
%Y A354551 Cf. A000248, A354550, A354552.
%K A354551 nonn
%O A354551 0,5
%A A354551 _Seiichi Manyama_, Aug 18 2022