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 A349846 #12 Dec 04 2021 06:41:00
%S A349846 -1,6,10,28,90,308,1092,3960,14586,54340,204204,772616,2939300,
%T A349846 11232648,43088200,165815280,639859770,2475036900,9593714460,
%U A349846 37255818600,144915581580,564514356120,2201964031800,8599360982160,33619842137700,131570223027048,515366318553912
%N A349846 Expansion of -(1 - 8*x) / sqrt(1 - 4*x).
%C A349846 Sum_{n>=0} (-a(n)/(-4)^n) is the Cauchy product of Sum_{n>=0} (-A349844(n)/(-8)^n) with itself.
%H A349846 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Cauchy_product">Cauchy product</a>
%F A349846 For n > 0, a(n) = 8*binomial(2*(n-1),n-1) - binomial(2*n,n) = binomial(2*(n-1),n-1) * (4 + 2/n).
%F A349846 a(n) ~ 4^n * (1/sqrt(Pi*n)).
%e A349846 a(1) = binomial(0,0) * (4 + 2/1) = 6;
%e A349846 a(2) = binomial(2,1) * (4 + 2/2) = 10;
%e A349846 a(3) = binomial(4,2) * (4 + 2/3) = 28;
%e A349846 a(4) = binomial(6,3) * (4 + 2/4) = 90.
%o A349846 (PARI) a(n) = if(n, binomial(2*(n-1),n-1) * (4 + 2/n), -1)
%Y A349846 Cf. A000984, A349844, A349835, A349847.
%K A349846 sign,easy
%O A349846 0,2
%A A349846 _Jianing Song_, Dec 01 2021