A201163 Expansion of g.f. 1+x+(1+3*x+x^2)/(1+x)^3.

2, 1, -2, 5, -9, 14, -20, 27, -35, 44, -54, 65, -77, 90, -104, 119, -135, 152, -170, 189, -209, 230, -252, 275, -299, 324, -350, 377, -405, 434, -464, 495, -527, 560, -594, 629, -665, 702, -740, 779, -819, 860, -902, 945, -989, 1034, -1080, 1127, -1175, 1224, -1274, 1325, -1377, 1430, -1484, 1539, -1595, 1652, -1710, 1769, -1829, 1890, -1952, 2015

Offset: 0

Author

N. J. A. Sloane, Nov 27 2011

Keywords

• sign
• easy

Links

• Vincenzo Librandi, 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.
• Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1).

Crossrefs

Cf. A000096.

Programs

Mathematica

Join[{2, 1}, LinearRecurrence[{-3, -3, -1}, {-2, 5, -9}, 70]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2012 *)
CoefficientList[Series[1+x+(1+3*x+x^2)/(1+x)^3,{x,0,70}],x] (* Harvey P. Dale, Aug 01 2020 *)

Formula

a(n) = (-1)^(n+1)*A000096(n-1), n>1. - R. J. Mathar, Nov 28 2011

Sum_{n>=0} 1/a(n) = 37/18 - 4*log(2)/3. - Amiram Eldar, Jan 31 2023