OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tian-Xiao He, Louis W. Shapiro, Row sums and alternating sums of Riordan arrays, Linear Algebra and its Applications, Volume 507, 15 October 2016, Pages 77-95. See R_3^{-}.
FORMULA
G.f.: 2*(1-sqrt(1-4*x))/(2*x)/(3-sqrt(1-4*x*(1-sqrt(1-4*x))/(2*x))). - Vincenzo Librandi, Apr 29 2017
Conjecture D-finite with recurrence: +126*n*(n-1)*(n+1)*a(n) -3*n*(n-1)*(691*n-1037)*a(n-1) +(n-1)*(12023*n^2-48049*n+47736)*a(n-2) +2*(-12889*n^3+93970*n^2-221427*n+169506)*a(n-3) +4*(-248*n^3+12718*n^2-88433*n+160113)*a(n-4) +16*(2918*n^3-41574*n^2+198532*n-317121)*a(n-5) +240*(4*n-19)*(2*n-9)*(4*n-21)*a(n-6)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
CoefficientList[Series[2 (1 - Sqrt[1 - 4 x]) / (2 x) / (3 - Sqrt[1 - 4 x (1 - Sqrt[1 - 4 x]) / (2 x)]), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 29 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Apr 28 2017
EXTENSIONS
More terms from Ilya Gutkovskiy, Apr 28 2017
STATUS
approved