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 A349847 #14 Jun 08 2023 13:00:12
%S A349847 1,10,22,68,230,812,2940,10824,40326,151580,573716,2183480,8347612,
%T A349847 32033848,123321400,476050320,1842020550,7142249340,27743985060,
%U A349847 107946346200,420608639220,1641030105000,6410161959240,25066222437360,98115049503900,384391435902552
%N A349847 Expansion of (1 + 8*x) / sqrt(1 - 4*x).
%C A349847 Sum_{n>=0} (a(n)/(-4)^n) is the Cauchy product of Sum_{n>=0} (-A349845(n)/8^n) with itself.
%H A349847 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Cauchy_product">Cauchy product</a>
%F A349847 For n > 0, a(n) = 8*binomial(2*(n-1),n-1) + binomial(2*n,n) = binomial(2*(n-1),n-1) * (12 - 2/n).
%F A349847 a(n) ~ 4^n * (3/sqrt(Pi*n)).
%e A349847 a(1) = binomial(0,0) * (12 - 2/1) = 10;
%e A349847 a(2) = binomial(2,1) * (12 - 2/2) = 22;
%e A349847 a(3) = binomial(4,2) * (12 - 2/3) = 68;
%e A349847 a(4) = binomial(6,3) * (12 - 2/4) = 230.
%t A349847 CoefficientList[Series[(1+8x)/Sqrt[1-4x],{x,0,30}],x] (* _Harvey P. Dale_, Jun 08 2023 *)
%o A349847 (PARI) a(n) = if(n, binomial(2*(n-1),n-1) * (12 - 2/n), 1)
%Y A349847 Cf. A000984, A349845, A349835, A349846.
%K A349847 nonn,easy
%O A349847 0,2
%A A349847 _Jianing Song_, Dec 01 2021