A025952 Expansion of 1/((1-2*x)*(1-3*x)*(1-9*x)*(1-10*x)).

1, 24, 385, 5220, 64741, 760944, 8633305, 95554140, 1038550381, 11132642664, 118050851425, 1241028864660, 12954973386421, 134451901289184, 1388638534032745, 14283461073576780, 146408292464020861, 1496246060581644504, 15251928830451105265, 155124502329708730500

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (24,-191,564,-540).

Formula

a(n) = -2^n/7+9*3^n/14-243*9^n/14+125*10^n/7. - R. J. Mathar, Jun 20 2013

a(n) = 3^(n+1)-2^(n+1)+19*a(n-1)-90*a(n-2). - Vincenzo Librandi, May 17 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-9x)(1-10x)), {x, 0, 20}], x] (* Harvey P. Dale, Dec 31 2021 *)
(* Alternative: *)
LinearRecurrence[{24, -191, 564, -540}, {1, 24, 385, 5220}, 20] (* Harvey P. Dale, Dec 31 2021 *)
(* Alternative: *)
a[0]=1; a[1]=24; a[n_]:=a[n]=3^(n+1)-2^(n+1)+19*a[n-1]-90*a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, May 17 2026 *)

Prog

(Magma) I:=[1, 24]; [n le 2 select I[n] else 3^n-2^n+19*Self(n-1)-90*Self(n-2): n in [1..22]]; // Vincenzo Librandi, May 17 2026

Crossrefs

Sequence in context: A266185 A114631 A020782 * A028031 A042108 A022455

Adjacent sequences: A025949 A025950 A025951 * A025953 A025954 A025955

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 17 2026

Status

approved