A021772 Expansion of 1/((1-x)(1-4x)(1-5x)(1-9x)).

1, 19, 242, 2618, 26103, 248997, 2316784, 21251956, 193359485, 1751044295, 15814841406, 142616378814, 1284983809747, 11572125768313, 104185847231708, 937857633325592, 8441649467754489, 75979521955403451

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19, -119, 281, -180).

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-9*x)).

a(0)=1, a(1)=19, a(2)=242, a(3)=2618, a(n)=19*a(n-1)-119*a(n-2)+ 281*a(n-3)- 180*a(n-4). - Harvey P. Dale, Jul 23 2011

a(n) = (3*9^(n+3)-30*5^(n+3)+32*4^(n+3)-5)/480. - Yahia Kahloune, May 23 2013.

Mathematica

CoefficientList[Series[1/((1-x)(1-4x)(1-5x)(1-9x)), {x, 0, 40}], x] (* or *) LinearRecurrence[{19, -119, 281, -180}, {1, 19, 242, 2618}, 41] (* Harvey P. Dale, Jul 23 2011 *)

Prog

(Magma) [(3*9^(n+3)-30*5^(n+3)+32*4^(n+3)-5)/480 : n in [0..30]]; // Wesley Ivan Hurt, Jun 12 2026

Crossrefs

Sequence in context: A025933 A107203 A021544 * A019783 A021504 A019512

Adjacent sequences: A021769 A021770 A021771 * A021773 A021774 A021775

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved