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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.

A362349 a(n) = n! * Sum_{k=0..floor(n/4)} k^k / (k! * (n-4*k)!).

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%I A362349 #15 Feb 16 2025 08:34:05
%S A362349 1,1,1,1,25,121,361,841,82321,728785,3633841,13313521,2195435881,
%T A362349 28125394441,196393341145,981274727161,227100486456481,
%U A362349 3807339471993121,34186011461595361,216366574074187105,64438384450412161081,1335035336388170601241
%N A362349 a(n) = n! * Sum_{k=0..floor(n/4)} k^k / (k! * (n-4*k)!).
%H A362349 Winston de Greef, <a href="/A362349/b362349.txt">Table of n, a(n) for n = 0..431</a>
%H A362349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362349 E.g.f.: exp(x) / (1 + LambertW(-x^4)).
%o A362349 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^4))))
%Y A362349 Cf. A086331, A362347, A362348.
%K A362349 nonn
%O A362349 0,5
%A A362349 _Seiichi Manyama_, Apr 17 2023