A028143 Expansion of 1/((1-4x)(1-6x)(1-10x)(1-12x)).

1, 32, 660, 11200, 170576, 2429952, 33121600, 437888000, 5663851776, 72087887872, 906450621440, 11292447129600, 139666259070976, 1717603091873792, 21027551488327680, 256495170125824000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (32, -364, 1728, -2880).

Formula

a(n)=(12^(n+3)-2*10^(n+3)+2*6^(n+3)-4^(n+3))/96. - Yahia Kahloune, Jun 11 2013

a(0)=1, a(1)=32, a(2)=660, a(3)=11200, a(n)=32*a(n-1)-364*a(n-2)+ 1728*a(n-3)- 2880*a(n-4). - Harvey P. Dale, Aug 15 2013

a(n) ~ 18*12^n. - Charles R Greathouse IV, Jun 02 2026

Mathematica

CoefficientList[Series[1/((1-4x)(1-6x)(1-10x)(1-12x)), {x, 0, 40}], x] (* Harvey P. Dale, Aug 15 2013 *)
(* Alternative: *)
LinearRecurrence[{32, -364, 1728, -2880}, {1, 32, 660, 11200}, 40] (* Harvey P. Dale, Aug 15 2013 *)

Prog

(PARI) a(n)=(108*12^n-125*10^n+27*6^n-4*4^n)/6 \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A028151 A160270 A028102 * A028101 A028097 A028021

Adjacent sequences: A028140 A028141 A028142 * A028144 A028145 A028146

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved