A025935 Expansion of 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-11*x)).

1, 21, 300, 3710, 43071, 485751, 5405170, 59772720, 659098341, 7258131881, 79879876440, 878881296930, 9668709132811, 106360879560411, 1169995084978110, 12870073026808340, 141571438884146481, 1557289006059043341, 17130194959478374180, 188432224021892338950, 2072754861589425099351

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-141,371,-330).

Formula

a(n) = 3^(n+3)/16+11^(n+3)/432-2^(n+3)/27-5^(n+3)/36. - R. J. Mathar, May 22 2013

a(n) = 3^(n+1)-2^(n+1)+16*a(n-1)-55*a(n-2). - Vincenzo Librandi, Apr 21 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-5*x)*(1-11*x)), {x, 0, 20}], x] (* Harvey P. Dale, Jan 04 2024 *)
(* Alternative: *)
LinearRecurrence[{21, -141, 371, -330}, {1, 21, 300, 3710}, 20] (* Harvey P. Dale, Jan 04 2024 *)
(* Alternative: *)
a[0]=1; a[1]=21; a[n_]:=a[n]=3^(n+1)-2^(n+1)+16*a[n-1]-55*a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Apr 21 2026 *)

Prog

(Magma) I:=[1, 21]; [n le 2 select I[n] else 3^n-2^n+16*Self(n-1)-55*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 21 2026

Crossrefs

Sequence in context: A295049 A295377 A021604 * A077506 A007592 A019664

Adjacent sequences: A025932 A025933 A025934 * A025936 A025937 A025938

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 21 2026

Status

approved