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%I #24 May 02 2023 09:00:54
%S 5,256,3159,65625,1114112,20421115,363484989,6542701056,117265259375,
%T 2105190412273,37769592176640,677792498259891,12162186734914229,
%U 218243684178400000,3916209628945328967,70273629018014076105,1261008431526362415104,22627882807257322061611,406040850098667041878125
%N a(n) = F(n+5)*F(n+2)^5, where F = Fibonacci (A000045).
%C The right-hand side of Helmut Postl's identity F(2*n+5) + F(n)*F(n+3)^5 = F(n+5)*F(n+2)^5.
%H Colin Barker, <a href="/A275930/b275930.txt">Table of n, a(n) for n = 0..750</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (13,104,-260,-260,104,13,-1).
%F From _Colin Barker_, Aug 31 2016: (Start)
%F a(n) = 13*a(n-1)+104*a(n-2)-260*a(n-3)-260*a(n-4)+104*a(n-5)+13*a(n-6)-a(n-7) for n>6 .
%F G.f.: (5+191*x-689*x^2-766*x^3+311*x^4+39*x^5-3*x^6) / ((1+x)*(1-18*x+x^2)*(1-3*x+x^2)*(1+7*x+x^2)).
%F (End)
%t Table[(Fibonacci[n + 5] Fibonacci[n + 2]^5), {n, 0, 20}] (* _Vincenzo Librandi_, Sep 02 2016 *)
%o (PARI) Vec((5+191*x-689*x^2-766*x^3+311*x^4+39*x^5-3*x^6)/((1+x)*(1-18*x+x^2)*(1-3*x+x^2)*(1+7*x+x^2)) + O(x^20)) \\ _Colin Barker_, Aug 31 2016
%o (Magma) [Fibonacci(n+5)*Fibonacci(n+2)^5: n in [0..25]]; // _Vincenzo Librandi_, Sep 92 2016
%Y Cf. A000045.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Aug 31 2016