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A104531 Expansion of (1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3).

%I A104531 #14 Jan 30 2020 21:29:15
%S A104531 1,4,24,148,920,5736,35808,223668,1397496,8732920,54575888,341082504,
%T A104531 2131706864,13322959888,83267756400,520420803060,3252620324280,
%U A104531 20328841669080,127055130786960,794094089779800,4963086293860560,31019282772508080,193870492861908480
%N A104531 Expansion of (1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3).
%C A104531 Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to 5^n.
%H A104531 Vincenzo Librandi, <a href="/A104531/b104531.txt">Table of n, a(n) for n = 0..200</a>
%F A104531 a(n) = 0^n + sum{k=0..n, 4^(k+1)*C(2n-1, n-k-1)*2*(k+1)/(n+k+1)}
%F A104531 D-finite with recurrence: 4*n*a(n) = (41*n-24)*a(n-1) - 50*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 17 2012
%F A104531 a(n) ~ 3*5^(2*n-1)/4^n. - _Vaclav Kotesovec_, Oct 17 2012
%t A104531 CoefficientList[Series[(1+Sqrt[1-4*x])/(5*Sqrt[1-4*x]-3), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%o A104531 (PARI) x='x+O('x^66); Vec((1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3)) \\ _Joerg Arndt_, May 13 2013
%Y A104531 Cf. A088218, A067336, A076025, A104530, A104532.
%K A104531 easy,nonn
%O A104531 0,2
%A A104531 _Paul Barry_, Mar 12 2005