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%I #20 May 20 2022 11:51:47
%S 0,5,800,30375,640000,9765625,121500000,1313046875,12800000000,
%T 115330078125,976562500000,7863818359375,60750000000000,
%U 453238525390625,3282617187500000,23174285888671875,160000000000000000,1083264923095703125
%N a(n) = 5^n * n^5.
%H Vincenzo Librandi, <a href="/A198402/b198402.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (30,-375,2500,-9375,18750,-15625).
%F G.f.: 5*x*(1 + 130*x + 1650*x^2 + 3250*x^3 + 625*x^4)/(1-5*x)^6. - _Colin Barker_, Apr 30 2013
%F E.g.f.: 5*x*(1 + 75*x + 625*x^2 + 1250*x^3 + 625*x^4)*exp(5*x). - _G. C. Greubel_, May 18 2022
%F a(n) = A000351(n)*A000584(n). - _Michel Marcus_, May 19 2022
%t With[{m = 5}, Table[n^m*m^n, {n, 0, 30}]] (* _G. C. Greubel_, May 18 2022 *)
%o (Magma) [5^n*n^5: n in [0..20]]
%o (PARI) a(n)=5^n*n^5 \\ _Charles R Greathouse IV_, Jul 06 2017
%o (SageMath) m=5; [n^m*m^n for n in (0..30)] # _G. C. Greubel_, May 18 2022
%Y Cf. A000351, A000584, A097206.
%Y Sequences of the form n^m*m^n: A001477 (m=1), A007758 (m=2), A062074 (m=3), A062075 (m=4), this sequence (m=5), A198403 (m=6), A098803 (m=7), A198404 (m=8), A198478 (m=9), A198479 (m=10), A098880 (m=11).
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Oct 27 2011
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