A248157 Expansion of (1 - 2*x^2)/(1 + x)^2. First column of Riordan triangle A248156.

1, -2, 1, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 34, -35, 36, -37, 38, -39, 40, -41, 42, -43, 44, -45, 46, -47, 48, -49, 50, -51, 52, -53, 54, -55, 56, -57

Offset

0,2

Links

Table of n, a(n) for n=0..60.

Index entries for linear recurrences with constant coefficients, signature (-2,-1).

Formula

O.g.f.: (1 - 2*x^2)/(1 + x)^2 = -2 + 4/(1+x) - 1/(1+x)^2.

a(n) = -2*delta(n,0) + (-1)^n*(3 - n), n >= 0, with Kronecker delta(n,0) = 1 if n=0 else 0.

a(0) = 1, a(n) = -2*a(n-1) - a(n-2), n >= 3, with a(1) = -2, a(2) = 1.

a(n) = A038608(n-3) = A097141(n-1), n>=3.

Mathematica

CoefficientList[Series[(1-2x^2)/(1+x)^2, {x, 0, 60}], x] (* or *) LinearRecurrence[{-2, -1}, {1, -2, 1}, 60] (* Harvey P. Dale, Aug 25 2023 *)

Prog

(PARI) Vec((1 - 2*x^2)/(1 + x)^2 + O(x^80)) \\ Michel Marcus, Oct 11 2014

Crossrefs

Cf. A248156 (row k=0).

Sequence in context: A062329 A022958 A023444 * A290428 A136868 A276066

Adjacent sequences: A248154 A248155 A248156 * A248158 A248159 A248160

Keyword

sign,easy,less

Author

Wolfdieter Lang, Oct 05 2014

Status

approved