A016864 a(n) = (5*n + 1)^4.

1, 1296, 14641, 65536, 194481, 456976, 923521, 1679616, 2825761, 4477456, 6765201, 9834496, 13845841, 18974736, 25411681, 33362176, 43046721, 54700816, 68574961, 84934656, 104060401, 126247696

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			a(0) = (5*0 + 1)^4 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Eric Weisstein's MathWorld, Polygamma Function.
• Wikipedia, Polygamma Function.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A016861, A016862, A016863.

Programs

Mathematica

Table[(5*n + 1)^4, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020*)
LinearRecurrence[{5,-10,10,-5,1},{1,1296,14641,65536,194481},30] (* Harvey P. Dale, Jul 22 2021 *)

Formula

Sum_{n>=0} 1/a(n) = polygamma(3, 1/5)/3750. - Amiram Eldar, Oct 02 2020

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, Oct 02 2020

G.f.: -(1+1291*x+8171*x^2+5281*x^3+256*x^4)/(-1+x)^5. - Wesley Ivan Hurt, Oct 02 2020