%I #19 Sep 08 2022 08:45:49

%S 0,1,131584,193739769,34360262656,1907353515625,50780008567296,

%T 814206940192849,9007199791611904,75047319391891761,

%U 500000005000000000,2779958669714828041,13311666671401304064,56227703544907942489

%N a(n) = n^10*(n^8 + 1)/2.

%H Vincenzo Librandi, <a href="/A170800/b170800.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).

%F G.f.: x*(1 + 131565*x + 191239844*x^2 + 30701706940*x^3 + 1287510524640*x^4 + 20228672856392*x^5 + 142998539385460*x^6 + 503354978422188*x^7 + 932692832164970*x^8 + 932692832164970*x^9 + 503354978422188*x^10 + 142998539385460*x^11 + 20228672856392*x^12 + 1287510524640*x^13 + 30701706940*x^14 +191239844*x^15 + 131565*x^16 + x^17)/(1-x)^19. - _Harvey P. Dale_, Jul 14 2013

%F E.g.f.: x*(2 + 131582*x + 64448340*x^2 + 2798841090*x^3 + 28958138070*x^4 + 110687273866*x^5 + 197462489280*x^6 + 189036065760*x^7 + 106175395800*x^8 + 37112163804*x^9 + 8391004908*x^10 + 1256328866*x^11 + 125854638*x^12 + 8408778*x^13 + 367200*x^14 + 9996*x^15 + 153*x^16 + x^17)*exp(x)/2. - _G. C. Greubel_, Oct 12 2019

%p seq(n^10*(n^8 +1)/2, n=0..20); # _G. C. Greubel_, Oct 11 2019

%t Table[n^10 (n^8+1)/2,{n,0,20}] (* _Harvey P. Dale_, Jul 14 2013 *)

%o (Magma)[n^10*(n^8+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011

%o (PARI) vector(21, m, (m-1)^10*((m-1)^8 + 1)/2) \\ _G. C. Greubel_, Oct 11 2019

%o (Sage) [n^10*(n^8 +1)/2 for n in (0..20)] # _G. C. Greubel_, Oct 11 2019

%o (GAP) List([0..20], n-> n^10*(n^8 +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), A170799 (m=7), this sequence (m=8), A170801 (m=9), A170802 (m=10).

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 11 2009