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A028000
Expansion of 1/((1-2*x)*(1-6*x)*(1-9*x)*(1-11*x)).
3
1, 28, 513, 7808, 107309, 1384836, 17143081, 206182696, 2429008197, 28183193324, 323282753729, 3676063130064, 41519535153565, 466480044231892, 5219284450672857, 58204869911960312, 647392469287421813, 7185592654453466940, 79620150969549450865, 881030260639705543840
OFFSET
0,2
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
KEYWORD
nonn,easy
STATUS
approved