A025941 Expansion of 1/((1-2*x)*(1-3*x)*(1-6*x)*(1-11*x)).

1, 22, 327, 4172, 49553, 567714, 6382699, 71043064, 786493125, 8681598926, 95678810591, 1053554778276, 11595631317817, 127591121803258, 1403737417995603, 15442522109891408, 169876206409453229, 1868689050095030310, 20555884229753339335, 226116554603020504060, 2487293069098086428961

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-157,432,-396).

Formula

a(n) = -2^(n+1)/9-3*6^(n+1)/5+11^(n+3)/360+3^(n+2)/8. - R. J. Mathar, Jun 04 2013

a(n) = 22*a(n-1)-157*a(n-2)+432*a(n-3)-396*a(n-4), with a(0)=1, a(1)=22, a(2)=327, a(3)=4172. - Harvey P. Dale, Aug 20 2014

a(n) = 3^(n+1)-2^(n+1)+17*a(n-1)-66*a(n-2). - Vincenzo Librandi, May 01 2026

E.g.f.: exp(2*x)*(1331*exp(9*x) - 1296*exp(4*x) + 405*exp(x) - 80)/360. - Stefano Spezia, May 04 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-6*x)*(1-11*x)), {x, 0, 20}], x] (* Harvey P. Dale, Aug 20 2014 *)
(* Alternative: *)
LinearRecurrence[{22, -157, 432, -396}, {1, 22, 327, 4172}, 20] (* Harvey P. Dale, Aug 20 2014 *)
(* Alternative: *)
a[0]=1; a[1]=22; a[n_]:=a[n]=3^(n+1)-2^(n+1)+17a[n-1]-66 a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, May 01 2026 *)

Prog

(Magma) I:=[1, 22]; [n le 2 select I[n] else 3^n-2^n+17*Self(n-1)-66*Self(n-2): n in [1..25]]; // Vincenzo Librandi, May 01 2026

Crossrefs

Sequence in context: A021874 A025963 A020343 * A125479 A047868 A002539

Adjacent sequences: A025938 A025939 A025940 * A025942 A025943 A025944

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 01 2026

Status

approved