A025968 Expansion of 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-10*x)).

1, 22, 320, 3920, 44016, 471072, 4904320, 50237440, 509670656, 5141007872, 51677982720, 518395637760, 5193684791296, 51995352604672, 520305091051520, 5205162447994880, 52064302294695936, 520719124195049472, 5207647986877726720, 52079220888095948800, 520808657195893784576

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,-164,488,-480).

Formula

a(n) = -2^n/8 +8*4^n/3-27*6^n/4+125*10^n/24. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2 + 16*a(n-1) - 60*a(n-2). - Vincenzo Librandi, Jun 11 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-6x)(1-10x)), {x, 0, 30}], x] (* Harvey P. Dale, Dec 30 2014 *)
(* Alternative: *)
LinearRecurrence[{22, -164, 488, -480}, {1, 22, 320, 3920}, 30] (* Harvey P. Dale, Dec 30 2014 *)

Prog

(Magma) I:=[1, 22]; [n le 2 select I[n] else (4^n-2^n)/2+16*Self(n-1)-60*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 11 2026

Crossrefs

Sequence in context: A025972 A028029 A022453 * A025948 A021904 A022343

Adjacent sequences: A025965 A025966 A025967 * A025969 A025970 A025971

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 11 2026

Status

approved