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%I #10 Aug 16 2015 12:04:01
%S 5,48510,465793515,4472549283020,42945417749765025,
%T 412361896760694487530,3959498889750770719498535,
%U 38019107927025003687930446040,365059470355795195660737423378045,3505300996337237541709397051345542550,33657899801770684519698434826282476187555
%N Positive pentagonal numbers (A000326) that are triangular numbers (A000217) divided by 2.
%H Colin Barker, <a href="/A259161/b259161.txt">Table of n, a(n) for n = 1..251</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9603,-9603,1).
%F G.f.: -5*x*(99*x+1) / ((x-1)*(x^2-9602*x+1)).
%e 5 is in the sequence because 5 is the 2nd pentagonal number, and 2*5 is the 4th triangular number.
%t LinearRecurrence[{9603, -9603, 1}, {5, 48510, 465793515}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)
%o (PARI) Vec(-5*x*(99*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))
%Y Cf. A000217, A000326, A074378, A259156-A259160, A259162-A259167.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jun 19 2015