A201164 - OEIS

%I #17 Mar 18 2020 14:51:12

%S -1,-1,0,2,9,30,95,299,955,3113,10360,35131,121073,423002,1494987,

%T 5335329,19199601,69587445,253789506,930660441,3429351837,12691395888,

%U 47151135165,175791361713,657484674168,2466239796855,9275575019799,34971114290258,132147593298213,500400210254835,1898537971954776,7216166900953283,27474327414227272

%N Expansion of g.f. -(1+x)*(1+sqrt(1-4*x))/(2*(1-x-x^2)).

%H G. C. Greubel, <a href="/A201164/b201164.txt">Table of n, a(n) for n = 0..1000</a>

%H Tian-Xiao He and Renzo Sprugnoli, <a href="https://doi.org/10.1016/j.disc.2008.11.021">Sequence characterization of Riordan arrays</a>, Discrete Math. 309 (2009), no. 12, 3962-3974.

%F a(n) ~ 5/11*4^n/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 29 2013

%F D-finite with recurrence: n*a(n) +4*(-n+1)*a(n-1) +2*(-n+5)*a(n-2) +(7*n-18)*a(n-3) +2*(2*n-7)*a(n-4)=0. - _R. J. Mathar_, Jan 25 2020

%t CoefficientList[Series[-(1 + x)*(1 + Sqrt[1 - 4*x])/(2*(1 - x - x^2)), {x,0,50}], x] (* _G. C. Greubel_, May 27 2017 *)

%o (PARI) my(x='x+O('x^50)); Vec(-(1+x)*(1+sqrt(1-4*x))/(2*(1-x-x^2))) \\ _G. C. Greubel_, May 27 2017

%K sign

%O 0,4

%A _N. J. A. Sloane_, Nov 27 2011