A201164 Expansion of g.f. -(1+x)*(1+sqrt(1-4*x))/(2*(1-x-x^2)).

-1, -1, 0, 2, 9, 30, 95, 299, 955, 3113, 10360, 35131, 121073, 423002, 1494987, 5335329, 19199601, 69587445, 253789506, 930660441, 3429351837, 12691395888, 47151135165, 175791361713, 657484674168, 2466239796855, 9275575019799, 34971114290258, 132147593298213, 500400210254835, 1898537971954776, 7216166900953283, 27474327414227272

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Tian-Xiao He and Renzo Sprugnoli, Sequence characterization of Riordan arrays, Discrete Math. 309 (2009), no. 12, 3962-3974.

Formula

a(n) ~ 5/11*4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A056283 A192518 A277241 * A289901 A261330 A101604

Adjacent sequences: A201161 A201162 A201163 * A201165 A201166 A201167

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2011

Status

approved