|
%I #31 Sep 08 2022 08:45:56
%S 1,3,10,34,118,418,1508,5524,20486,76722,289580,1099836,4198396,
%T 16093236,61902472,238805864,923574598,3579675026,13900879132,
%U 54071886764,210645038548,821701422716,3209243934712,12547819633304,49109812222108,192382627198868
%N Row sums of the Riordan matrix (1/sqrt(1-4*x), x/(1-x)) (A187888).
%H G. C. Greubel, <a href="/A188622/b188622.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%F D-finite with recurrence: (n+3)*a(n+3) - (7*n+17)*a(n+2) + 2*(7*n+12)*a(n+1) - 4*(2*n+1)*a(n) = 0.
%F G.f.: (1-x)/((1-2*x)*sqrt(1-4*x)).
%t CoefficientList[Series[(1-x)/((1-2x)Sqrt[1-4x]),{x,0,30}],x] (* _Harvey P. Dale_, Oct 25 2016 *)
%o (Maxima) a(n):=at(diff((1-x)/((1-2*x)*sqrt(1-4*x)),x,n),x=0)/n!;
%o makelist(a(n),n,0,24);
%o (PARI) x='x+O('x^30); Vec((1-x)/((1-2*x)*sqrt(1-4*x))) \\ _G. C. Greubel_, Nov 01 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x)/((1-2*x)*Sqrt(1-4*x)))); // _G. C. Greubel_, Nov 01 2018
%Y Cf. A187888
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Apr 06 2011
%E More terms from _Harvey P. Dale_, Oct 25 2016
|
