login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = (6*n + 3)^5.
8

%I #18 Mar 30 2022 06:34:23

%S 243,59049,759375,4084101,14348907,39135393,90224199,184528125,

%T 345025251,601692057,992436543,1564031349,2373046875,3486784401,

%U 4984209207,6956883693,9509900499,12762815625,16850581551,21924480357,28153056843,35723051649,44840334375,55730836701

%N a(n) = (6*n + 3)^5.

%H Vincenzo Librandi, <a href="/A016949/b016949.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F From _Amiram Eldar_, Mar 30 2022: (Start)

%F a(n) = A016945(n)^5.

%F a(n) = 3^5*A016757(n).

%F Sum_{n>=0} 1/a(n) = 31*zeta(5)/7776.

%F Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/373248. (End)

%t a[n_] := (6*n + 3)^5; Array[a, 50, 0] (* _Amiram Eldar_, Mar 30 2022 *)

%o (Magma) [(6*n+3)^5: n in [0..50]]; // _Vincenzo Librandi_, May 05 2011

%Y Cf. A016757, A016945, A016946, A016947, A016948.

%Y Subsequence of A000584.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_