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 A346398 #18 Jul 23 2025 09:07:37
%S A346398 0,1,-5,20,-72,249,-825,2736,-8568,29385,-74709,417636,698544,
%T A346398 21853233,244181223,3608612208,54277152624,878859416817,
%U A346398 15072037479099,273539358115092,5235734703888648,105419854939796937,2227408664800976487,49278475088626210704,1139260699549648412856
%N A346398 Expansion of e.g.f. -log(1 - x) * exp(-3*x).
%H A346398 Seiichi Manyama, <a href="/A346398/b346398.txt">Table of n, a(n) for n = 0..451</a>
%F A346398 a(n) = n! * Sum_{k=0..n-1} (-3)^k / ((n-k) * k!).
%F A346398 a(0) = 0, a(1) = 1, a(n) = (n-4) * a(n-1) + 3 * (n-1) * a(n-2) + (-3)^(n-1). - _Seiichi Manyama_, May 27 2022
%F A346398 a(n) ~ exp(-3) * (n-1)!. - _Vaclav Kotesovec_, Jun 08 2022
%t A346398 nmax = 24; CoefficientList[Series[-Log[1 - x] Exp[-3 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A346398 Table[n! Sum[(-3)^k/((n - k) k!), {k, 0, n - 1}], {n, 0, 24}]
%o A346398 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(i-4)*v[i]+3*(i-1)*v[i-1]+(-3)^(i-1)); v; \\ _Seiichi Manyama_, May 27 2022
%Y A346398 Cf. A002741, A010843, A346397.
%K A346398 sign
%O A346398 0,3
%A A346398 _Ilya Gutkovskiy_, Jul 15 2021