A022456 Expansion of 1/((1-x)*(1-5*x)*(1-7*x)*(1-12*x)).

1, 25, 422, 6074, 80739, 1027731, 12764344, 156290788, 1897808357, 22932373997, 276311410986, 3323658428142, 39939656787655, 479667696880423, 5758762699959548, 69124442908248536, 829628539194983433

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-203,599,-420).

Formula

a(n) = (2*12^(n+4) - 22*7^(n+4) + 33*5^(n+4) - 35)/9240. - Yahia Kahloune, Jun 27 2013

a(0)=1, a(1)=25, a(2)=422, a(3)=6074; for n > 3, a(n) = 25*a(n-1) - 203*a(n-2) + 599*a(n-3) - 420*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2012 *)
LinearRecurrence[{25, -203, 599, -420}, {1, 25, 422, 6074}, 30] (* Harvey P. Dale, Jul 22 2015 *)

Prog

(Magma) I:=[1, 25, 422, 6074]; [n le 4 select I[n] else 25*Self(n-1)-203*Self(n-2)+599*Self(n-3)-420*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-7*x)*(1-12*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-7*x)*(1-12*x))) \\ G. C. Greubel, Feb 28 2018

Crossrefs

Sequence in context: A020595 A001456 A021964 * A020593 A025951 A021944

Adjacent sequences: A022453 A022454 A022455 * A022457 A022458 A022459

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved