A025955 Expansion of 1/((1-2*x)*(1-3*x)*(1-10*x)*(1-11*x)).

1, 26, 455, 6760, 92121, 1191606, 14892475, 181671620, 2176950941, 25732149586, 300910712895, 3488589043680, 40160193084961, 459619264745966, 5234383334635715, 59363930948274940, 670860383232854181, 7558035643966852746, 84924106368851684935, 952022312913017317400, 10650816870610136578601

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-221,676,-660).

Formula

a(n) = -2^n/9+27*3^n/56-125*10^n/7+1331*11^n/72. - R. J. Mathar, Jun 20 2013

a(0)=1, a(1)=26, a(2)=455, a(3)=6760, a(n) = 26*a(n-1)-221*a(n-2)+676*a(n-3)-660*a(n-4). - Harvey P. Dale, Aug 25 2014

a(n) = 3^(n+1)-2^(n+1)+21*a(n-1)-110*a(n-2). - Vincenzo Librandi, May 26 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-10*x)*(1-11*x)), {x, 0, 20}], x] (* Harvey P. Dale, Aug 25 2014 *)
(* Alternative: *)
LinearRecurrence[{26, -221, 676, -660}, {1, 26, 455, 6760}, 20] (* Harvey P. Dale, Aug 25 2014 *)
(* Alternative: *)
a[0]=1; a[1]=26; a[n_]:=a[n]=3^(n+1)-2^(n+1)+21*a[n-1]-110*a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, May 26 2026 *)

Prog

(Magma) I:=[1, 26]; [n le 2 select I[n] else 3^n-2^n+21*Self(n-1)-110*Self(n-2): n in [1..21]]; // Vincenzo Librandi, May 26 2026

Crossrefs

Sequence in context: A020970 A023953 A020968 * A022725 A020606 A021984

Adjacent sequences: A025952 A025953 A025954 * A025956 A025957 A025958

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 26 2026

Status

approved