A269550 Expansion of (-5*x^2 + 228*x - 7)/(x^3 - 99*x^2 + 99*x - 1).

7, 465, 45347, 4443325, 435400287, 42664784585, 4180713488827, 409667257120245, 40143210484294967, 3933624960203786305, 385455102889486762707, 37770666458209498958765, 3701139857801641411196047, 362673935398102648798253625, 35538344529156257940817658987

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 d_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, A269551, A269552, A269553, A269554, A269555, A269556.

Programs

Magma

I:=[7,465,45347]; [n le 3 select I[n]  else 99*Self(n-1)+-99*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Feb 29 2016

Mathematica

LinearRecurrence[{99, -99, 1}, {7, 465, 45347}, 20] (* Vincenzo Librandi, Feb 29 2016 *)

PARI

Vec((-5*x^2 + 228*x - 7)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))