A025951 Expansion of 1/((1-2*x)*(1-3*x)*(1-8*x)*(1-12*x)).

1, 25, 423, 6125, 82103, 1054725, 13214671, 163046125, 1992333255, 24194295125, 292622085119, 3529789897725, 42504079369207, 511221761969125, 6144043634254767, 73803583579040525, 886243482821361959, 10639725633226507125, 127715138314841131615, 1532889105510563684125, 18397128831996983303511

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-202,600,-576).

Formula

a(n) = -2*2^n/15+3*3^n/5-64*8^n/15+24*12^n/5. - R. J. Mathar, Jun 20 2013

a(0)=1, a(1)=25, a(2)=423, a(3)=6125, a(n) = 25*a(n-1)-202*a(n-2)+600*a(n-3)-576*a(n-4). - Harvey P. Dale, Mar 08 2014

a(n) = 3^(n+1)-2^(n+1)+20*a(n-1)-96*a(n-2). - Vincenzo Librandi, May 14 2026

Maple

A025951:=n->-2*2^n/15+3*3^n/5-64*8^n/15+24*12^n/5; seq(A025951(n), n=0..30); # Wesley Ivan Hurt, Mar 10 2014

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-8*x)*(1-12*x)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 08 2014 *)
(* Alternative: *)
LinearRecurrence[{25, -202, 600, -576}, {1, 25, 423, 6125}, 30] (* Harvey P. Dale, Mar 08 2014 *)
(* Alternative: *)
a[0]=1; a[1]=25; a[n_]:=a[n]=3^(n+1)-2^(n+1)+20*a[n-1]-96*a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, May 14 2026 *)

Prog

(Magma) I:=[1, 25]; [n le 2 select I[n] else 3^n-2^n+20*Self(n-1)-96*Self(n-2): n in [1..22]]; // Vincenzo Librandi, May 14 2026

Crossrefs

Sequence in context: A021964 A022456 A020593 * A021944 A299845 A020499

Adjacent sequences: A025948 A025949 A025950 * A025952 A025953 A025954

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 14 2026

Status

approved