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%I #21 Jan 27 2018 13:31:15
%S 1,45,1085,20925,366141,6120765,100080445,1618667325,26038501181,
%T 417737748285,6692790374205,107156587499325,1715081133346621,
%U 27445904805580605,439171333486530365,7027036201446788925,112434938199985606461,1798977883220621905725
%N Expansion of (1 + 14*x) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)*(1 - 16*x)).
%H Colin Barker, <a href="/A177728/b177728.txt">Table of n, a(n) for n = 0..800</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (31,-310,1240,-1984,1024).
%F G.f.: (1 + 14*x) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)*(1 - 16*x)). - _Colin Barker_, Nov 27 2012
%F From _Colin Barker_, Jan 27 2018: (Start)
%F a(n) = (1/21)*((-1 + 2^(1+n))^2*(1-3*2^(2+n) + 2^(5+2*n))).
%F a(n) = 31*a(n-1) - 310*a(n-2) + 1240*a(n-3) - 1984*a(n-4) + 1024*a(n-5) for n>4.
%F (End)
%o (PARI) Vec((1 + 14*x) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)*(1 - 16*x)) + O(x^40)) \\ _Colin Barker_, Jan 27 2018
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, May 12 2010
%E New name using g.f. given by _Colin Barker_ from _Joerg Arndt_, Jan 27 2018