A016091 Expansion of 1/((1-8x)(1-9x)(1-10x)(1-12x)).

1, 39, 955, 18795, 325171, 5167659, 77353795, 1107933915, 15345293491, 207057429579, 2736619356835, 35572444360635, 456191563128211, 5785999811488299, 72719715037363075, 907085298655532955

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (39,-566,3624,-8640).

Formula

From Vincenzo Librandi, Mar 17 2011: (Start)

a(n) = 39*a(n-1) - 566*a(n-2) + 3624*a(n-3) - 8640*a(n-4) for n >= 4.

a(n) = 22*a(n-1) - 120*a(n-2) + 9^(n+1) - 8^(n+1) for n >= 2. (End)

a(n) = -8^(n+2) + 3*9^(n+2) - 25*10^(n+1) + 6*12^(n+1). - R. J. Mathar, Mar 18 2011

E.g.f.: exp(8*x)*(72*exp(4*x) - 250*exp(2*x) + 243*exp(x) - 64). - Stefano Spezia, Aug 14 2022

Mathematica

CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)
LinearRecurrence[{39, -566, 3624, -8640}, {1, 39, 955, 18795}, 30] (* Harvey P. Dale, Jul 08 2019 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-10*x)*(1-12*x)))); /* or */ I:=[1, 39, 955, 18795]; [n le 4 select I[n] else 39*Self(n-1)-566*Self(n-2)+3624*Self(n-3)-8640*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Jun 24 2013

Crossrefs

Sequence in context: A004330 A069418 A194477 * A028227 A028219 A209076

Adjacent sequences: A016088 A016089 A016090 * A016092 A016093 A016094

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved