A025969 Expansion of 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-11*x)).

1, 23, 353, 4603, 55449, 640851, 7242961, 80866811, 896831177, 9909444259, 109271790849, 1203605509899, 13249389022585, 145801783940147, 1604171188346417, 17647994609290267, 194140618516940073, 2135622904934430915, 23492308699205972065, 258418136710584374315

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-176,532,-528).

Formula

a(0)=1, a(1)=23, a(2)=353, a(3)=4603, a(n) = 23*a(n-1)-176*a(n-2)+532*a(n-3)-528*a(n-4). - Harvey P. Dale, Jun 25 2011

a(n) = (8*11^(n+3)-63*6^(n+3)+90*4^(n+3)-35*2^(n+3))/2520. - Yahia Kahloune, May 24 2013

a(n) = (4^(n+1)-2^(n+1))/2+17*a(n-1)-66*a(n-2). - Vincenzo Librandi, Jun 18 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-6x)(1-11x)), {x, 0, 40}], x] (* Harvey P. Dale, Jun 25 2011 *)
(* Alternative: *)
LinearRecurrence[ {23, -176, 532, -528}, {1, 23, 353, 4603}, 40] (* Harvey P. Dale, Jun 25 2011 *)
(* Alternative: *)
a[0]=1; a[1]=23; Do[a[n]=(4^(n+1)-2^(n+1))/2+17*a[n-1]-66*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 19}] (* Vincenzo Librandi, Jun 18 2026 *)

Prog

(Magma) I:=[1, 23]; [n le 2 select I[n] else (4^n-2^n)/2+17*Self(n-1)-66*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 18 2026

Crossrefs

Sequence in context: A022454 A142617 A025949 * A020579 A021914 A022412

Adjacent sequences: A025966 A025967 A025968 * A025970 A025971 A025972

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 18 2026

Status

approved