A021214 Expansion of 1/((1-x)*(1-2x)*(1-6x)*(1-12x)).

1, 21, 313, 4137, 51961, 637497, 7733881, 93310329, 1122747001, 13491103353, 162002078329, 1944677972601, 23340053875321, 280104155744889, 3361390924417657, 40337537425951353, 484055527109184121

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (21,-128,252,-144).

Formula

a(n) = (2*12^(n+3) - 11*6^(n+3) + 33*2^(n+3) - 24)/1320. - Yahia Kahloune, May 19 2013

a(0)=1, a(1)=21, a(2)=313, a(3)=4137; for n>3, a(n) = 21*a(n-1) -128*a(n-2) +252*a(n-3)-144*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -72*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{21, -128, 252, -144}, {1, 21, 313, 4137}, 30] (* Harvey P. Dale, Mar 07 2015 *)

Prog

(Magma) I:=[1, 21, 313, 4137]; [n le 4 select I[n] else 21*Self(n-1)-128*Self(n-2)+252*Self(n-3)-144*Self(n-4): n in [1..25]]; /* or */ I:=[1, 21]; [n le 2 select I[n] else 18*Self(n-1)-72*Self(n-2)+2^n-1: n in [1..20]]; // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A226990 A016321 A019041 * A016318 A017954 A055434

Adjacent sequences: A021211 A021212 A021213 * A021215 A021216 A021217

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved