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 A330045 #21 Nov 20 2022 02:02:17
%S A330045 1,1,1,1,25,121,361,841,42001,365905,1819441,6660721,498971881,
%T A330045 6278929801,43710250585,218205219961,21795091762081,358652470233121,
%U A330045 3210080802962401,20298322381652065,2534333270094778681,51516840824285500441,563561785768079119561
%N A330045 Expansion of e.g.f. exp(x) / (1 - x^4).
%H A330045 Seiichi Manyama, <a href="/A330045/b330045.txt">Table of n, a(n) for n = 0..450</a>
%F A330045 G.f.: Sum_{k>=0} (4*k)! * x^(4*k) / (1 - x)^(4*k + 1).
%F A330045 a(0) = a(1) = a(2) = a(3) = 1; a(n) = n*(n - 1)*(n - 2)*(n - 3)*a(n - 4) + 1.
%F A330045 a(n) = Sum_{k=0..floor(n/4)} n! / (n - 4*k)!.
%F A330045 a(n) ~ n! * (2*cos(Pi*n/2 - 1) + exp(1) + (-1)^n*exp(-1))/4. - _Vaclav Kotesovec_, Apr 18 2020
%t A330045 nmax = 22; CoefficientList[Series[Exp[x]/(1 - x^4), {x, 0, nmax}], x] Range[0, nmax]!
%t A330045 Table[Sum[n!/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
%Y A330045 Cf. A000522, A087208, A100733, A330044, A334157.
%Y A330045 Outer diagonal of A158777.
%K A330045 nonn
%O A330045 0,5
%A A330045 _Ilya Gutkovskiy_, Nov 28 2019