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 A346752 #15 Dec 15 2023 09:09:53
%S A346752 0,0,0,0,1,5,15,35,35,-504,-6090,-45870,-265155,-990275,2733731,
%T A346752 113064315,1571621870,15859846380,116145112140,289646855916,
%U A346752 -9965576133855,-255337210989315,-4024508801328785,-47031887951290165,-338016913616223534,1717029492398463650
%N A346752 Expansion of e.g.f. log( 1 + x^4 * exp(x) / 4! ).
%H A346752 Seiichi Manyama, <a href="/A346752/b346752.txt">Table of n, a(n) for n = 0..487</a>
%F A346752 a(0) = 0; a(n) = binomial(n,4) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * binomial(n-k,4) * k * a(k).
%F A346752 a(n) = n! * Sum_{k=1..floor(n/4)} (-1)^(k-1) * k^(n-4*k-1)/(24^k * (n-4*k)!). - _Seiichi Manyama_, Dec 14 2023
%t A346752 nmax = 25; CoefficientList[Series[Log[1 + x^4 Exp[x]/4!], {x, 0, nmax}], x] Range[0, nmax]!
%t A346752 a[0] = 0; a[n_] := a[n] = Binomial[n, 4] - (1/n) Sum[Binomial[n, k] Binomial[n - k, 4] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 25}]
%Y A346752 Cf. A000332, A009306, A145454, A346750, A346751, A346755.
%K A346752 sign
%O A346752 0,6
%A A346752 _Ilya Gutkovskiy_, Aug 01 2021