A025963 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-11*x)).

1, 22, 325, 4110, 48381, 550062, 6148165, 68149870, 752379661, 8290355502, 91266902805, 1004309278830, 11049302357341, 121551961591342, 1337120292662245, 14708568942522990, 161795495573813421, 1779756671701857582, 19577354628108674485, 215351057655891914350

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..930

Index entries for linear recurrences with constant coefficients, signature (22,-159,458,-440).

Formula

a(n) = -4*2^n/27+32*4^n/7-125*5^n/18+1331*11^n/378. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2+16*a(n-1)-55*a(n-2). - Vincenzo Librandi, Jun 04 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-11*x)), {x, 0, 30}], x] (* Harvey P. Dale, Jul 16 2016 *)
(* Alternative: *)
LinearRecurrence[{22, -159, 458, -440}, {1, 22, 325, 4110}, 30] (* Harvey P. Dale, Jul 16 2016 *)
(* Alternative: *)
a[0]=1; a[1]=22; Do[a[n]=(4^(n+1)-2^(n+1))/2+16*a[n-1]-55*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Jun 04 2026 *)

Prog

(Magma) I:=[1, 22]; [n le 2 select I[n] else (4^n-2^n)/2+16*Self(n-1)-55*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 04 2026

Crossrefs

Sequence in context: A288576 A020571 A021874 * A020343 A025941 A125479

Adjacent sequences: A025960 A025961 A025962 * A025964 A025965 A025966

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 04 2026

Status

approved