A025982 Expansion of 1/((1-2*x)*(1-4*x)*(1-9*x)*(1-12*x)).

1, 27, 487, 7431, 103951, 1382439, 17812639, 224794647, 2797053391, 34460823111, 421597615231, 5131789410423, 62235068724271, 752703321093543, 9085382857597663, 109501083478899159, 1318301413026203791, 15858212692188777735, 190645914066573014335, 2290877225191400595255

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (27,-242,816,-864).

Formula

a(n) = 27*a(n-1) - 242*a(n-2) + 816*a(n-3) - 864*a(n-4), a(0)=1, a(1)=27, a(2)=487, a(3)=7431. - Harvey P. Dale, Jul 21 2012

a(n) = -2*2^n/35 + 4*4^n/5 - 243*9^n/35 + 36*12^n/5. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2+21*a(n-1)-108*a(n-2). - Vincenzo Librandi, Jul 02 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-9x)(1-12x)), {x, 0, 30}], x] (* Harvey P. Dale, Jul 21 2012 *)
(* Alternative: *)
LinearRecurrence[{27, -242, 816, -864}, {1, 27, 487, 7431}, 30] (* Harvey P. Dale, Jul 21 2012 *)

Prog

(Magma) I:=[1, 27]; [n le 2 select I[n] else (4^n-2^n)/2+21*Self(n-1)-108*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jul 02 2026

Crossrefs

Sequence in context: A081139 A020976 A024114 * A042408 A023946 A020971

Adjacent sequences: A025979 A025980 A025981 * A025983 A025984 A025985

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jul 02 2026

Status

approved