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%I #21 Sep 08 2022 08:45:49
%S 0,1,16896,7203978,537395200,15263671875,235122725376,2373921992596,
%T 17592722915328,102947309439525,500005000000000,2088637053420126,
%U 7703541745975296,25593015436291303,77784192406233600
%N a(n) = n^10*(n^5+1)/2.
%H Vincenzo Librandi, <a href="/A170797/b170797.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F G.f.: x*(15872*x^13 +6890977*x^12 +423932400*x^11 +7520863426*x^10 +51389080880*x^9 +155692452591*x^8 +223769408736*x^7 +155695145820*x^6 +51387918048*x^5 +7520366095*x^4 +424158512*x^3 +6933762*x^2 +16880*x +1) / (x-1)^16. - _Colin Barker_, Nov 01 2014
%F a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16) for n > 15. - _Wesley Ivan Hurt_, Aug 10 2016
%F E.g.f.: x*(2 +16894*x +2384431*x^2 +42390055*x^3 +210809445*x^4 + 420716100*x^5 +408747213*x^6 +216628590*x^7 +67128535*x^8 +12662651*x^9 +1479478*x^10 +106470*x^11 +4550*x^12 +105*x^13 +x^14)*exp(x)/2. - _G. C. Greubel_, Oct 11 2019
%p A170797:=n->n^10*(n^5+1)/2: seq(A170797(n), n=0..20); # _Wesley Ivan Hurt_, Aug 10 2016
%t Table[n^10*(n^5 + 1)/2, {n, 0, 15}] (* _Wesley Ivan Hurt_, Aug 10 2016 *)
%o (Magma)[n^10*(n^5+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 26 2011
%o (PARI) vector(21, m, (m-1)^10*((m-1)^5 + 1)/2) \\ _G. C. Greubel_, Oct 11 2019
%o (Sage) [n^10*(n^5 +1)/2 for n in (0..20)] # _G. C. Greubel_, Oct 11 2019
%o (GAP) List([0..20], n-> n^10*(n^5 +1)/2); # _G. C. Greubel_, Oct 11 2019
%Y Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), this sequence (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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