A285195 G.f.: 2C(x)/(3-sqrt(1-4xC(x))) where C = g.f. for A000108.

1, 0, 0, -1, -6, -30, -142, -660, -3054, -14154, -65886, -308442, -1452940, -6887508, -32852082, -157630609, -760599954, -3689418510, -17984138984, -88063955880, -433048404780, -2137792856760, -10591472304270, -52648861274730, -262514740621860, -1312653157205088, -6580914381986160

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

Sequence in context: A137400 A220830 A199938 * A307321 A026749 A003279

Adjacent sequences: A285192 A285193 A285194 * A285196 A285197 A285198

Keyword

sign

Author

N. J. A. Sloane, Apr 28 2017

Extensions

More terms from Ilya Gutkovskiy, Apr 28 2017

Status

approved