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%I #19 Mar 31 2022 03:09:15
%S 16,625,4096,14641,38416,83521,160000,279841,456976,707281,1048576,
%T 1500625,2085136,2825761,3748096,4879681,6250000,7890481,9834496,
%U 12117361,14776336,17850625,21381376,25411681,29986576,35153041,40960000,47458321,54700816,62742241,71639296
%N a(n) = (3*n+2)^4.
%H Vincenzo Librandi, <a href="/A016792/b016792.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _Ilya Gutkovskiy_, Jun 16 2016: (Start)
%F G.f.: (16 + 545*x + 1131*x^2 + 251*x^3 + x^4)/(1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)
%F From _Amiram Eldar_, Mar 31 2022: (Start)
%F a(n) = A016789(n)^4 = A016790(n)^2.
%F Sum_{n>=0} 1/a(n) = PolyGamma(3, 2/3)/486. (End)
%t Table[(3n+2)^4,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)
%t LinearRecurrence[{5,-10,10,-5,1},{16,625,4096,14641,38416},30] (* _Harvey P. Dale_, Aug 02 2018 *)
%o (Magma) [(3*n+2)^4 : n in [0..30]]; // _Vincenzo Librandi_, Sep 29 2011
%Y Cf. A016789, A016790, A016791.
%Y Subsequence of A000583.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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