A021694 Expansion of 1/((1-x)(1-3x)(1-9x)(1-11x)).

1, 24, 394, 5544, 71995, 891408, 10701748, 125788848, 1456313749, 16673208552, 189289198462, 2135136588312, 23963101915663, 267883518461856, 2985323286760936, 33185997429018336, 368172943255604137

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (24,-182,456,-297).

Crossrefs

Cf. A006100, A018091 (first differences).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-9*x)*(1-11*x)))); // Bruno Berselli, May 07 2013

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *)
LinearRecurrence[{24,-182,456,-297},{1,24,394,5544},20] (* Harvey P. Dale, Mar 01 2022 *)

PARI

Vec(1/((1-x)*(1-3*x)*(1-9*x)*(1-11*x))+O(x^20)) \\ Bruno Berselli, May 07 2013

Formula

G.f.: 1/((1-x)*(1-3*x)*(1-9*x)*(1-11*x)).

a(n) = -1/160 +3^(n+2)/32 -3^(2n+5)/32 +11^(n+3)/160. [Bruno Berselli, May 07 2013]

a(n)-11*a(n-1) = A006100(n+2). [Bruno Berselli, May 08 2013]