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%I #9 Jun 13 2015 00:54:38
%S 1032,54472,853256,8392840,64852872,433408392,2632152456,14947110280,
%T 80788946312,420521631112,2125121035656,10487138557320,50753701289352,
%U 241670439050632,1135046330686856,5268615489133960,24208077521689992,110246366797634952
%N The hyper-Wiener index of the dendrimer NS[n], defined pictorially in the A. R. Ashrafi et al. reference.
%C a(1) has been checked by the direct computation of the Wiener index (using Maple).
%D A. R. Ashrafi and M. Mirzargar, The study of an infinite class of dendrimer nanostars by topological index approaches, J. Appl. Math. Comput, 31, 2009, 289-294.
%D M. J. Nadjafi-Arani, A new algorithm for computing the Wiener index of molecular graphs (unpublished paper).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-86,232,-288,128).
%F a(n) = 7560 - 64000*4^n*n - 113312*2^n + 106784*4^n + 25600*4^n*n^2.
%F G.f.: 8*(129+4874*x+15616*x^2+4896*x^3)/((1-x)*(1-2*x)*(1-4*x)^3). [_Bruno Berselli_, Apr 06 2013]
%p a := proc (n) options operator, arrow: 7560-113312*2^n+25600*4^n*n^2-64000*4^n*n+106784*4^n end proc: seq(a(n), n = 0 .. 18);
%t CoefficientList[Series[8 (129 + 4874 x + 15616 x^2 + 4896 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)^3), {x, 0, 20}], x] (* _Bruno Berselli_, Apr 06 2013 *)
%Y Cf. A224427.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Apr 06 2013
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