A269552 Expansion of (-3*x^2 + 94*x - 3)/(x^3 - 99*x^2 + 99*x - 1).

3, 203, 19803, 1940403, 190139603, 18631740603, 1825720439403, 178901971320803, 17530567468999203, 1717816709990601003, 168328507011609899003, 16494475870427779501203, 1616290306794910781218803, 158379955590030828779941403, 15519619357516226309653038603, 1520764317081000147517217841603

Offset: 0

Author

Michel Marcus, Feb 29 2016

Keywords

• nonn
• easy

Comments

Mc Laughlin (2010) gives an identity relating ten sequences, denoted a_k, b_k, ..., f_k, p_k, q_k, r_k, s_k. This is the sequence f_k.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• J. Mc Laughlin, An identity motivated by an amazing identity of Ramanujan, Fib. Q., 48 (No. 1, 2010), 34-38.
• Index entries for linear recurrences with constant coefficients, signature (99, -99, 1).

Crossrefs

Cf. A010701, A261004, A269548, A269549, A269550, A269551, A269553, A269554, A269555, A269556.

Programs

Mathematica

CoefficientList[Series[(-3x^2+94x-3)/(x^3-99x^2+99x-1),{x,0,20}],x] (* or *) LinearRecurrence[{99,-99,1},{3,203,19803},20] (* Harvey P. Dale, Jan 14 2019 *)

PARI

Vec((-3*x^2 + 94*x - 3)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))

Formula

G.f.: (-3*x^2 + 94*x - 3)/(x^3 - 99*x^2 + 99*x - 1).

a(n) = 99*a(n-1)-99*a(n-2)+a(n-3). - Wesley Ivan Hurt, May 20 2021