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%I A016780 #30 Mar 29 2022 03:21:38
%S A016780 1,256,2401,10000,28561,65536,130321,234256,390625,614656,923521,
%T A016780 1336336,1874161,2560000,3418801,4477456,5764801,7311616,9150625,
%U A016780 11316496,13845841,16777216,20151121,24010000,28398241,33362176,38950081,45212176,52200625,59969536,68574961
%N A016780 a(n) = (3*n+1)^4.
%H A016780 Vincenzo Librandi, <a href="/A016780/b016780.txt">Table of n, a(n) for n = 0..10000</a>
%H A016780 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A016780 From _Harvey P. Dale_, Oct 21 2015: (Start)
%F A016780 a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5).
%F A016780 G.f.: -((1+251*x+1131*x^2+545*x^3+16*x^4)/(-1+x)^5). (End)
%F A016780 a(n) = A000583(A016777(n)). - _Michel Marcus_, Nov 06 2015
%F A016780 E.g.f.: exp(x)*(1+255*x+945*x^2+594*x^3+81*x^4). - _Wolfdieter Lang_, Apr 02 2017
%F A016780 Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/3)/486. - _Amiram Eldar_, Mar 29 2022
%t A016780 (3*Range[0,30]+1)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,256,2401,10000,28561},30] (* _Harvey P. Dale_, Oct 21 2015 *)
%o A016780 (Magma) [(3*n+1)^4: n in [0..30]]; // _Vincenzo Librandi_, Sep 21 2011
%Y A016780 Cf. A000583 (n^4), A016777 (3n+1), A016778, A016779, A016781.
%K A016780 nonn,easy
%O A016780 0,2
%A A016780 _N. J. A. Sloane_.

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