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 A209832 #24 Oct 09 2023 10:00:41
%S A209832 1,2,12,200,6576,353312,28032192,3077502080,446470392576,
%T A209832 82695752049152,19038594625539072,5332477132779407360,
%U A209832 1785375992372231909376,704147423230177089953792,323094378183013059349757952,170643791820813252598723543040
%N A209832 Expansion of the q-series Sum_{n>=0} (-1)^n*q^(n+1)*Product_{k = 1..n} (1 - q^(2*k-1)), q = exp(t), as a formal Taylor series in t.
%C A209832 Compare with A158690.
%H A209832 Vaclav Kotesovec, <a href="/A209832/b209832.txt">Table of n, a(n) for n = 0..200</a>
%H A209832 Hsien-Kuei Hwang, Emma Yu Jin, <a href="https://arxiv.org/abs/1911.06690">Asymptotics and statistics on Fishburn matrices and their generalizations</a>, arXiv:1911.06690 [math.CO], 2019.
%F A209832 E.g.f.: Sum_{n>=0} exp((n+1)*t) * Product_{k = 1..n} (exp((2*k-1)*t) - 1) = exp(t) + exp(2*t)*(exp(t) - 1) + exp(3*t)*(exp(t) - 1)*(exp(3*t) - 1) + ... = 1 + 2*t + 12*t^2/2! + 200*t^3/3! + ...
%F A209832 Conjectural S-fraction expansion for the o.g.f.:
%F A209832 1/(1-2*x/(1-4*x/(1-16*x/(1-20*x/(1-...-2*n(3*n-2)*x/(1-2*n(3*n-1)*x/(1-...
%F A209832 a(n) ~ 2^(3*n + 2) * 3^(n + 1/2) * n^(2*n + 1/2) / (exp(2*n) * Pi^(2*n + 1/2)). - _Vaclav Kotesovec_, Oct 09 2023
%t A209832 nmax = 20; CoefficientList[Series[Sum[(-1)^n*Exp[x*(n + 1)] * Product[ (1 - Exp[(2*k - 1)*x]), {k, 1, n}], {n, 0, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 09 2023 *)
%Y A209832 Cf. A158690.
%K A209832 nonn,easy
%O A209832 0,2
%A A209832 _Peter Bala_, Mar 14 2012