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A168636 a(n) = n^7*(n^2 + 1)/2.

%I A168636 #17 Mar 24 2025 09:27:31
%S A168636 0,1,320,10935,139264,1015625,5178816,20588575,68157440,196101729,
%T A168636 505000000,1188717431,2597806080,5333623945,10383230144,19307109375,
%U A168636 34493956096,59499107585,99485755200,161790784759,256640000000,398040567561,604881787840,902278743455
%N A168636 a(n) = n^7*(n^2 + 1)/2.
%H A168636 G. C. Greubel, <a href="/A168636/b168636.txt">Table of n, a(n) for n = 0..1000</a>
%H A168636 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A168636 From _Harvey P. Dale_, Mar 09 2016: (Start)
%F A168636 a(0)=0, a(1)=1, a(2)=320, a(3)=10935, a(4)=139264, a(5)=1015625, a(6)=5178816, a(7)=20588575, a(8)=68157440, a(9)=196101729, a(n)= 10*a(n-1)- 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).
%F A168636 G.f.: x*(1 + 310*x + 7780*x^2 + 44194*x^3 + 76870*x^4 + 44194*x^5 + 7780*x^6 + 310*x^7 + x^8)/(1 - x)^10. (End)
%F A168636 E.g.f.: (1/2)*x*(2 + 318*x + 3326*x^2 + 8120*x^3 + 7091*x^4 + 2667*x^5 + 463*x^6 + 36*x^7 + x^8)*exp(x). - _G. C. Greubel_, Jul 28 2016
%t A168636 Table[n^7 (n^2+1)/2,{n,0,20}] (* or *) LinearRecurrence[{10,-45,120,-210, 252, -210, 120, -45,10,-1}, {0,1, 320, 10935, 139264, 1015625, 5178816, 20588575, 68157440, 196101729}, 21] (* _Harvey P. Dale_, Mar 09 2016 *)
%o A168636 (Magma) [n^7*(n^2+1)/2: n in [0..25]]; // _Vincenzo Librandi_, Jul 29 2016
%o A168636 (PARI) a(n)=n^7*(n^2+1)/2 \\ _Charles R Greathouse IV_, Jul 29 2016
%o A168636 (SageMath)
%o A168636 def A168636(n): return n^5*binomial(n^2+1,2)
%o A168636 print([A168636(n) for n in range(31)]) # _G. C. Greubel_, Mar 23 2025
%Y A168636 Cf. A168635.
%K A168636 nonn,easy
%O A168636 0,3
%A A168636 _N. J. A. Sloane_, Dec 11 2009