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 A346397 #17 Jul 23 2025 09:07:41
%S A346397 0,1,-3,8,-18,44,-80,272,112,5280,38464,414336,4573184,55680000,
%T A346397 731374592,10335551488,156303374336,2518984953856,43099088904192,
%U A346397 780268881068032,14902336355991552,299452809651617792,6315501510330286080,139485953831281098752,3219718099932087844864
%N A346397 Expansion of e.g.f. -log(1 - x) * exp(-2*x).
%H A346397 Seiichi Manyama, <a href="/A346397/b346397.txt">Table of n, a(n) for n = 0..451</a>
%F A346397 a(n) = n! * Sum_{k=0..n-1} (-2)^k / ((n-k) * k!).
%F A346397 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A002741(k).
%F A346397 a(0) = 0, a(1) = 1, a(n) = (n-3) * a(n-1) + 2 * (n-1) * a(n-2) + (-2)^(n-1). - _Seiichi Manyama_, May 27 2022
%F A346397 a(n) ~ exp(-2) * (n-1)!. - _Vaclav Kotesovec_, Jun 08 2022
%t A346397 nmax = 24; CoefficientList[Series[-Log[1 - x] Exp[-2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A346397 Table[n! Sum[(-2)^k/((n - k) k!), {k, 0, n - 1}], {n, 0, 24}]
%o A346397 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(i-3)*v[i]+2*(i-1)*v[i-1]+(-2)^(i-1)); v; \\ _Seiichi Manyama_, May 27 2022
%Y A346397 Cf. A000023, A002741, A335111, A346398.
%K A346397 sign
%O A346397 0,3
%A A346397 _Ilya Gutkovskiy_, Jul 15 2021