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%I #28 Sep 08 2022 08:46:01
%S 1,36,3585,73810,669921,3784176,15721201,52683870,150652545,381367036,
%T 876543201,1862778666,3709924705,6996023880,12592235601,21771494326,
%U 36344967681,58830704340,92659184065,142420804866,214160664801,315726318496
%N 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8.
%C The n for which a(n) is prime begin: n = 174, 414, 474, 516, 546, 594, 714, 756, 804, 1386, 1596, 1734, 1806, 1986, 2514. - _Joerg Arndt_, Jan 15 2013
%H G. C. Greubel, <a href="/A209267/b209267.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: (6*x^8 +1371*x^7 +27991*x^6 +115317*x^5 +131793*x^4 +42757*x^3 +3297*x^2 +27*x +1) / (1-x)^9. - _Colin Barker_, Jan 26 2013
%e a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 + 5*2^5 + 6*2^6 + 7*2^7 + 8*2^8 = 3585.
%t Table[Total[Table[i*n^i,{i,2,8}]]+1,{n,0,30}] (* _Harvey P. Dale_, Jan 26 2013 *)
%o (Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8,n,0,20); /* _Martin Ettl_, Jan 15 2013 */
%o (PARI) for(n=0,30, print1(1 + sum(k=2,8, k*n^k), ", ")) \\ _G. C. Greubel_, Jan 05 2018
%o (Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8: n in [0..30]]; // _G. C. Greubel_, Jan 05 2018
%Y Cf. A209262, A209263, A209264, A209265.
%K nonn,easy
%O 0,2
%A _Jonathan Vos Post_, Jan 15 2013
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