%I #24 Sep 08 2022 08:45:49

%S 0,1,66048,64599606,8590458880,381474609375,8463359955456,

%T 116315398231228,1125900443713536,8338592593225485,50000005000000000,

%U 252723527218359186,1109305584328900608,4325208028619914891,15245673509292925440,49263062956171875000,147573953139432226816

%N a(n) = n^10*(n^7 + 1)/2.

%H Vincenzo Librandi, <a href="/A170799/b170799.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

%F G.f.: x*(65024*x^15 + 63370125*x^14 + 7437628950*x^13 + 236677103915*x^12 + 2858645957220*x^11 + 15527824213413*x^10 + 41568614867330*x^9 + 57445190329275*x^8 + 41568608318040*x^7 + 15527828734975*x^6 + 2858646015162*x^5 + 236676197145*x^4 + 7437770500*x^3 + 63410895*x^2 + 66030*x + 1)/(x-1)^18. - _Colin Barker_, Feb 24 2013

%F E.g.f.: x*(2 + 66046*x + 21467155*x^2 + 694371395*x^3 + 5652794176*x^4 + 17505772725*x^5 + 25708110666*x^6 + 20415995778*x^7 + 9528822348*x^8 + 2758334151*x^9 + 512060978*x^10 + 62022324*x^11 + 4910178*x^12 + 249900*x^13 + 7820*x^14 + 136*x^15 + x^16)*exp(x)/2. - _G. C. Greubel_, Oct 12 2019

%p seq(n^10*(n^7 +1)/2, n=0..20); # _G. C. Greubel_, Oct 11 2019

%t Table[n^10(n^7+1)/2,{n,0,20}] (* _Harvey P. Dale_, Aug 27 2013 *)

%o (Magma)[n^10*(n^7+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011

%o (PARI) vector(21, m, (m-1)^10*((m-1)^7 + 1)/2) \\ _G. C. Greubel_, Oct 11 2019

%o (Sage) [n^10*(n^7 +1)/2 for n in (0..20)] # _G. C. Greubel_, Oct 11 2019

%o (GAP) List([0..20], n-> n^10*(n^7 +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), A170797 (m=5), A170798 (m=6), this sequence (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