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 A357836 #13 Feb 16 2025 08:34:04
%S A357836 0,0,1,-3,11,-49,259,-1589,11109,-87171,758121,-7229859,74905467,
%T A357836 -836159961,9980000667,-126422745813,1686902233653,-23512989735963,
%U A357836 338917341235473,-4982536435536387,73087736506615467,-1025163078325255233,12286912220375608179
%N A357836 a(n) = Sum_{k=0..floor((n-2)/3)} Stirling1(n,3*k+2).
%H A357836 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PochhammerSymbol.html">Pochhammer Symbol</a>.
%F A357836 Let w = exp(2*Pi*i/3) and set F(x) = (exp(x) + w*exp(w*x) + w^2*exp(w^2*x))/3 = x^2/2! + x^5/5! + x^8/8! + ... . Then the e.g.f. for the sequence is F(log(1+x)).
%F A357836 a(n) = (-1)^n * ( (-1)_n + w * (-w)_n + w^2 * (-w^2)_n )/3, where (x)_n is the Pochhammer symbol.
%o A357836 (PARI) a(n) = sum(k=0, (n-2)\3, stirling(n, 3*k+2, 1));
%o A357836 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(sum(k=0, N\3, log(1+x)^(3*k+2)/(3*k+2)!))))
%o A357836 (PARI) Pochhammer(x, n) = prod(k=0, n-1, x+k);
%o A357836 a(n) = my(w=(-1+sqrt(3)*I)/2); (-1)^n*round(Pochhammer(-1, n)+w*Pochhammer(-w, n)+w^2*Pochhammer(-w^2, n))/3;
%Y A357836 Cf. A357834, A357835.
%K A357836 sign
%O A357836 0,4
%A A357836 _Seiichi Manyama_, Oct 14 2022