A021964 Expansion of 1/((1-x)(1-4x)(1-9x)(1-11x)).

1, 25, 422, 6050, 79563, 993675, 12002224, 141692500, 1645717205, 18887136125, 214818117306, 2426541462150, 27263857999327, 305049644712175, 3401871310224068, 37837512809631800, 419965002207076329

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,-203,575,-396).

Formula

a(n) = (12*11^(n+3) - 21*9^(n+3) + 4^(n+5) - 7)/1680. - Yahia Kahloune, Jun 26 2013

a(0)=1, a(1)=25, a(2)=422, a(3)=6050; for n>3, a(n) = 25*a(n-1) -203*a(n-2) +575*a(n-3) -396*a(n-4). - Vincenzo Librandi, Jul 11 2013

a(0)=1, a(1)=25; for n>1, a(n) = 20*a(n-1) -99*a(n-2) +(4^n - 1)/3. - Vincenzo Librandi, Jul 11 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{25, -203, 575, -396}, {1, 25, 422, 6050}, 20] (* Harvey P. Dale, Aug 24 2021 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 25, 422, 6050]; [n le 4 select I[n] else 25*Self(n-1)-203*Self(n-2)+575*Self(n-3)-396*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013

Crossrefs

Sequence in context: A025953 A020595 A001456 * A022456 A020593 A025951

Adjacent sequences: A021961 A021962 A021963 * A021965 A021966 A021967

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved