A016864 - OEIS

%I #21 Jul 08 2025 05:57:13

%S 1,1296,14641,65536,194481,456976,923521,1679616,2825761,4477456,

%T 6765201,9834496,13845841,18974736,25411681,33362176,43046721,

%U 54700816,68574961,84934656,104060401,126247696

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

%H Amiram Eldar, <a href="/A016864/b016864.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygamma_function">Polygamma Function</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F Sum_{n>=0} 1/a(n) = polygamma(3, 1/5)/3750. - _Amiram Eldar_, Oct 02 2020

%F 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

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

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

%t Table[(5*n + 1)^4, {n, 0, 25}] (* _Amiram Eldar_, Oct 02 2020*)

%t LinearRecurrence[{5,-10,10,-5,1},{1,1296,14641,65536,194481},30] (* _Harvey P. Dale_, Jul 22 2021 *)

%Y Cf. A016861, A016862, A016863.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_