A016817 a(n) = (4n+1)^5.

1, 3125, 59049, 371293, 1419857, 4084101, 9765625, 20511149, 39135393, 69343957, 115856201, 184528125, 282475249, 418195493, 601692057, 844596301, 1160290625, 1564031349, 2073071593, 2706784157, 3486784401, 4437053125, 5584059449, 6956883693, 8587340257, 10510100501

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A013663, A016813.

Programs

Mathematica

Table[(4n+1)^5,{n,0,100}] (* Mohammad K. Azarian, Jun 18 2016 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{1,3125,59049,371293,1419857,4084101},30] (* Harvey P. Dale, Oct 02 2022 *)

Formula

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Apr 12 2023

From Amiram Eldar, Apr 21 2023: (Start)

a(n) = A016813(n)^5.

Sum_{n>=0} 1/a(n) = 5*Pi^5/3072 + 31*zeta(5)/64. (End)