A028000 Expansion of 1/((1-2x)(1-6x)(1-9x)(1-11x)).

1, 28, 513, 7808, 107309, 1384836, 17143081, 206182696, 2429008197, 28183193324, 323282753729, 3676063130064, 41519535153565, 466480044231892, 5219284450672857, 58204869911960312, 647392469287421813

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (28, -271, 1032, -1188).

Formula

a(n) = (14*11^(n+3)-30*9^(n+3)+21*6^(n+3)-5*2^(n+3))/1260 . [Yahia Kahloune, Jun 05 2013]

In general,for the expansion of 1/((1-r*x)(1-s*x)(1-t*x)(1-u*x) with u>t>s>r, we have the formula: a(n) =[G(u)*u^(n+3) - G(t)*t^(n+3) + G(s)*s^(n+3)- G(r)*r^(n+3)]/[G(u)*G(t)*G(s)*G(r)]^(1/2). In which G(u)=(t-s)*(t-r)*(s-r); G(t) =(u-s)*(u-r)*(s-r); G(s) =(u-t)*(u-r)*(t-r); G(r) =(u-t)*(u-s)*(t-s). [Yahia Kahloune, Sep 10 2013]

a(n) = 28*a(n-1) - 271*a(n-2) + 1032*a(n-3) - 1188*a(n-4) for n>3. - Vincenzo Librandi, Jun 03 2014

Mathematica

CoefficientList[Series[1/((1 - 2 x) (1 - 6 x) (1 - 9 x) (1 - 11 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(Magma) I:=[1, 28, 513, 7808]; [n le 4 select I[n] else 28*Self(n-1)-271*Self(n-2)+1032*Self(n-3)-1188*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 03 2014

Crossrefs

Sequence in context: A028069 A028007 A028078 * A028067 A024771 A028050

Adjacent sequences: A027997 A027998 A027999 * A028001 A028002 A028003

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved