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 A346751 #15 Dec 15 2023 09:09:57
%S A346751 0,0,0,1,4,10,10,-105,-1064,-6076,-16680,129525,2642860,25431406,
%T A346751 130210444,-639438345,-26431524560,-382074099000,-3083015556624,
%U A346751 5641134587049,726952330301940,14940678486798610,173111303303845060,258953439321230731,-43858702741534022936
%N A346751 Expansion of e.g.f. log( 1 + x^3 * exp(x) / 3! ).
%H A346751 Seiichi Manyama, <a href="/A346751/b346751.txt">Table of n, a(n) for n = 0..471</a>
%F A346751 a(0) = 0; a(n) = binomial(n,3) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * binomial(n-k,3) * k * a(k).
%F A346751 a(n) = n! * Sum_{k=1..floor(n/3)} (-1)^(k-1) * k^(n-3*k-1)/(6^k * (n-3*k)!). - _Seiichi Manyama_, Dec 14 2023
%t A346751 nmax = 24; CoefficientList[Series[Log[1 + x^3 Exp[x]/3!], {x, 0, nmax}], x] Range[0, nmax]!
%t A346751 a[0] = 0; a[n_] := a[n] = Binomial[n, 3] - (1/n) Sum[Binomial[n, k] Binomial[n - k, 3] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 24}]
%Y A346751 Cf. A000292, A009306, A145453, A346750, A346752, A346754.
%K A346751 sign
%O A346751 0,5
%A A346751 _Ilya Gutkovskiy_, Aug 01 2021