login
a(n) = (4n)^8.
1

%I #19 Sep 08 2022 08:44:41

%S 0,65536,16777216,429981696,4294967296,25600000000,110075314176,

%T 377801998336,1099511627776,2821109907456,6553600000000,

%U 14048223625216,28179280429056,53459728531456,96717311574016,167961600000000,281474976710656,457163239653376

%N a(n) = (4n)^8.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F a(0)=0, a(1)=65536, a(2)=16777216, a(3)=429981696, a(4)=4294967296, a(5)=25600000000, a(6)=110075314176, a(7)=377801998336, a(8)=1099511627776, a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)- 126*a(n-4)+126*a(n-5)-84*a(n-6)+ 36*a(n-7)- 9*a(n-8)+a(n-9). - _Harvey P. Dale_, Aug 05 2013

%F G.f.: 65536*(x + 247*x^2 + 4293*x^3 + 15619*x^4 + 15619*x^5 + 4293*x^6 + 247*x^7 + x^8)/(1 - x)^9. - _Wesley Ivan Hurt_, Mar 18 2015

%F a(n) = A001016(A008586(n)). - _Michel Marcus_, Mar 18 2015

%p A016808:=n->(4*n)^8: seq(A016808(n), n=0..30); # _Wesley Ivan Hurt_, Mar 18 2015

%t (4*Range[0,20])^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,65536,16777216,429981696,4294967296,25600000000,110075314176,377801998336,1099511627776},20] (* _Harvey P. Dale_, Aug 05 2013 *)

%t CoefficientList[Series[65536 (x + 247 x^2 + 4293 x^3 + 15619 x^4 + 15619 x^5 + 4293 x^6 + 247 x^7 + x^8) / (1 - x)^9, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 18 2015 *)

%o (Magma) [(4*n)^8: n in [0..30]]; // _Vincenzo Librandi_, Mar 18 2015

%Y Cf. A001016 (n^8), A008586 (4*n).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_