A022845 Expansion of 1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)).

1, 25, 416, 5810, 73731, 881895, 10139746, 113382280, 1242174461, 13399350965, 142804173876, 1507398751950, 15788505813991, 164317248669235, 1701069830850806, 17531812552906820, 180008344463520321

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,-209,635,-450).

Formula

a(n) = (32*10^(n+3) - 45*9^(n+3) + 18*5^(n+3) - 5)/1440. - Yahia Kahloune, Jun 29 2013

a(0)=1, a(1)=25, a(2)=416, a(3)=5810; for n>3, a(n) = 25*a(n-1) -209*a(n-2) +635*a(n-3) -450*a(n-4). - Vincenzo Librandi, Jul 12 2013

Maple

seq(coeff(series(((1-x)*(1-5*x)*(1-9*x)*(1-10*x))^(-1), x, n+1), x, n), n = 0..20); # Muniru A Asiru, Sep 28 2018

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)))); /* or /* I:=[1, 25, 416, 5810]; [n le 4 select I[n] else 25*Self(n-1)-209*Self(n-2)+635*Self(n-3)-450*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x))) \\ G. C. Greubel, Sep 28 2018

Crossrefs

Sequence in context: A025978 A028037 A102072 * A023952 A025991 A022628

Adjacent sequences: A022842 A022843 A022844 * A022846 A022847 A022848

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved