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 A357939 #13 Jul 22 2025 15:13:53
%S A357939 1,0,0,1,0,1,1,1,3,2,7,7,16,26,41,92,128,317,478,1107,1977,4077,8547,
%T A357939 16310,37775,71489,170660,339138,795833,1705058,3876254,8926023,
%U A357939 19888522,48187837,107726407,267597455,613509355,1531527270,3646775589,9066267823
%N A357939 a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k).
%F A357939 G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x^2).
%t A357939 Table[Sum[StirlingS2[k,n-2k],{k,0,Floor[n/2]}],{n,0,40}] (* _Harvey P. Dale_, Jul 22 2025 *)
%o A357939 (PARI) a(n) = sum(k=0, n\2, stirling(k, n-2*k, 2));
%o A357939 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/prod(j=1, k, 1-j*x^2)))
%Y A357939 Cf. A357940, A357941.
%Y A357939 Cf. A357903.
%K A357939 nonn
%O A357939 0,9
%A A357939 _Seiichi Manyama_, Oct 21 2022