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A168661 a(n) = n^7*(n^4 + 1)/2.

%I A168661 #16 Mar 24 2025 12:54:08
%S A168661 0,1,1088,89667,2105344,24453125,181538496,989075143,4296015872,
%T A168661 15692921289,50005000000,142665578891,371522101248,896111571277,
%U A168661 2024835291584,4324963359375,8796227239936,17136153323153,32134511149632,58245576384979,102400640000000,175139650815381,292160397884608
%N A168661 a(n) = n^7*(n^4 + 1)/2.
%H A168661 Vincenzo Librandi, <a href="/A168661/b168661.txt">Table of n, a(n) for n = 0..10000</a>
%H A168661 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A168661 From _G. C. Greubel_, Jul 28 2016: (Start)
%F A168661 G.f.: x*(1 + 1076*x + 76677*x^2 + 1100928*x^3 + 4868154*x^4 + 7864728*x^5 + 4868154*x^6 + 1100928*x^7 + 76677*x^8 + 1076*x^9 + x^10)/(1 - x)^12.
%F A168661 E.g.f.: (1/2)*x*(2 + 1086*x + 28802*x^2 + 146100*x^3 + 246870*x^4 + 179508*x^5 + 63988*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)
%t A168661 Table[n^7*(n^4 + 1)/2, {n,0,25}] (* _G. C. Greubel_, Jul 28 2016 *)
%o A168661 (Magma) [n^7*(n^4+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011
%o A168661 (PARI) a(n)=n^7*(n^4+1)/2 \\ _Charles R Greathouse IV_, Jul 29 2016
%o A168661 (SageMath)
%o A168661 def A168661(n): return n^3*binomial(n^4+1,2)
%o A168661 print([A168661(n) for n in range(31)]) # _G. C. Greubel_, Mar 24 2025
%Y A168661 Cf. A168635.
%K A168661 nonn,easy
%O A168661 0,3
%A A168661 _N. J. A. Sloane_, Dec 11 2009