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 A104530 #14 Sep 01 2024 17:12:19
%S A104530 1,3,15,78,411,2178,11574,61596,328083,1748346,9319650,49688004,
%T A104530 264943902,1412826132,7534329804,40180417848,214285867011,
%U A104530 1142822599722,6094924220394,32505784870068,173362418710506,924593002335612,4931138212856244,26299312319336328,140262655976846766
%N A104530 Expansion of (1+sqrt(1-4x))/(4sqrt(1-4x)-2).
%C A104530 Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to 4^n.
%H A104530 Vincenzo Librandi, <a href="/A104530/b104530.txt">Table of n, a(n) for n = 0..200</a>
%F A104530 a(n) = 0^n + Sum_{k=0..n} 3^(k+1)*C(2*n-1, n-k-1)*2*(k+1)/(n+k+1).
%F A104530 Recurrence: 3*n*a(n) = 2*(14*n-9)*a(n-1) - 32*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 17 2012
%F A104530 a(n) ~ 2^(4*n-1)/3^n. - _Vaclav Kotesovec_, Oct 17 2012
%t A104530 CoefficientList[Series[(1+Sqrt[1-4*x])/(4*Sqrt[1-4*x]-2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%o A104530 (PARI) x='x+O('x^66); Vec((1+sqrt(1-4*x))/(4*sqrt(1-4*x)-2)) \\ _Joerg Arndt_, May 13 2013
%Y A104530 Cf. A088218, A067336, A076025.
%K A104530 easy,nonn
%O A104530 0,2
%A A104530 _Paul Barry_, Mar 12 2005