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 A357829 #13 Feb 16 2025 08:34:04
%S A357829 0,1,1,2,7,34,205,1456,11837,108150,1096011,12196128,147814359,
%T A357829 1938062490,27333191613,412614191808,6638401596645,113398127795862,
%U A357829 2049808094564139,39091473755006400,784404343854767727,16520634668922810426,364400233756422553053
%N A357829 a(n) = Sum_{k=0..floor((n-1)/3)} |Stirling1(n,3*k+1)|.
%H A357829 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PochhammerSymbol.html">Pochhammer Symbol</a>.
%F A357829 Let w = exp(2*Pi*i/3) and set F(x) = (exp(x) + w^2*exp(w*x) + w*exp(w^2*x))/3 = x + x^4/4! + x^7/7! + ... . Then the e.g.f. for the sequence is F(-log(1-x)).
%F A357829 a(n) = ( (1)_n + w^2 * (w)_n + w * (w^2)_n )/3, where (x)_n is the Pochhammer symbol.
%o A357829 (PARI) a(n) = sum(k=0, (n-1)\3, abs(stirling(n, 3*k+1, 1)));
%o A357829 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, N\3, (-log(1-x))^(3*k+1)/(3*k+1)!))))
%o A357829 (PARI) Pochhammer(x, n) = prod(k=0, n-1, x+k);
%o A357829 a(n) = my(w=(-1+sqrt(3)*I)/2); round(Pochhammer(1, n)+w^2*Pochhammer(w, n)+w*Pochhammer(w^2, n))/3;
%Y A357829 Cf. A357828, A357830.
%K A357829 nonn
%O A357829 0,4
%A A357829 _Seiichi Manyama_, Oct 14 2022