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%I #38 Mar 29 2022 02:59:56
%S 1,1024,16807,100000,371293,1048576,2476099,5153632,9765625,17210368,
%T 28629151,45435424,69343957,102400000,147008443,205962976,282475249,
%U 380204032,503284375,656356768,844596301,1073741824,1350125107,1680700000,2073071593,2535525376
%N a(n) = (3*n+1)^5.
%C In general the e.g.f. of {(1 + 3*m)^n}_{m>=0} is E(n,x) = exp(x)*Sum_{m=0..n} A282629(n, m)*x^m, and the o.g.f. is G(n, x) = (Sum_{m=0..n} A225117(n, n-m}*x^m)/(1-x)^(n+1). - _Wolfdieter Lang_, Apr 02 2017
%H Vincenzo Librandi, <a href="/A016781/b016781.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F 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). - _Harvey P. Dale_, May 13 2012
%F From _Wolfdieter Lang_, Apr 02 2017: (Start)
%F O.g.f.: (1+1018*x+10678*x^2+14498*x^3+2933*x^4+32*x^5)/(1-x)^6.
%F E.g.f: exp(x)*(1+1023*x+7380*x^2+8775*x^3+2835*x^4+243*x^5). (End)
%F a(n) = A000584(A016777(n)). - _Michel Marcus_, Apr 06 2017
%F Sum_{n>=0} 1/a(n) = 2*Pi^5/(3^6*sqrt(3)) + 121*zeta(5)/3^5. - _Amiram Eldar_, Mar 29 2022
%t (3Range[0,20]+1)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,1024,16807,100000,371293,1048576},30] (* _Harvey P. Dale_, May 13 2012 *)
%o (Magma) [(3*n+1)^5: n in [0..30]]; // _Vincenzo Librandi_, Sep 21 2011
%o (Maxima) A016781(n):=(3*n+1)^5$
%o makelist(A016781(n),n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%Y Cf. A016777, A016778, A016779, A016780, A225117, A282629.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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