A021054 Expansion of 1/((1-x)(1-2x)(1-3x)(1-11x)).

1, 17, 212, 2422, 26943, 297339, 3273754, 36020624, 396255365, 4358895541, 47948112576, 527430027306, 5801732675467, 63819066571823, 702009753747878, 7722107355665668, 84943181105770449, 934374992744081385

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-77,127,-66).

Formula

a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -33*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=17, a(2)=212, a(3)=2422; for n>3, a(n) = 17*a(n-1) -77*a(n-2) +127*a(n-3) -66*a(n-4). - Vincenzo Librandi, Jul 05 2013

a(n) = (11^(n+3) -45*3^(n+3) + 80*2^(n+3) - 36)/720. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-11*x)))); /* or */ I:=[1, 17, 212, 2422]; [n le 4 select I[n] else 17*Self(n-1)-77*Self(n-2)+127*Self(n-3)-66*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A016250 A255819 A070137 * A016246 A009441 A016293

Adjacent sequences: A021051 A021052 A021053 * A021055 A021056 A021057

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved