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a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8 + 9*n^9.
1

%I #21 Sep 08 2022 08:46:01

%S 1,45,8193,250957,3029217,21362301,106420465,415866333,1358612097,

%T 3868151437,9876543201,23084307885,50147947873,102436518237,

%U 198541656657,367761728701,654820258305,1126121592813,1877892797377,3046610084877

%N a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8 + 9*n^9.

%C The smallest prime here is a(12) = 50147947873.

%H G. C. Greubel, <a href="/A209275/b209275.txt">Table of n, a(n) for n = 0..5000</a>

%H <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 G.f.: (3*x^9 +3153*x^8 +104852*x^7 +706780*x^6 +1389234*x^5 +883142*x^4 +170932*x^3 +7788*x^2 +35*x +1) / (x -1)^10. - _Colin Barker_, Apr 19 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 + 9*2^9 = 8193.

%t Table[Total[Table[i*n^i,{i,2,9}]]+1,{n,0,30}] (* _Harvey P. Dale_, Jan 26 2013 *)

%o (PARI) for(n=0,30, print1(1 + sum(k=2,9, k*n^k), ", ")) \\ _G. C. Greubel_, Jan 04 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 + 9*n^9: n in [0..30]]; // _G. C. Greubel_, Jan 04 2018

%Y Cf. A209262, A209263, A209264, A209265, A209267.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Jan 15 2013