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%I #8 Nov 21 2013 12:48:46
%S 1,55,9217,280483,3378745,23803711,118513705,462945547,1512003793,
%T 4303999495,10987654321,25678050355,55776799177,113924725903,
%U 220792014745,408951042331,728121033505,1252121211607,2087920281313
%N 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8 + 10*n^9.
%C 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7*x^6 + 8*x^7 + 9*x^8 + 10*x^9 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 = (x^11 - 1)/(x-1).
%F a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8 + 10*n^9.
%F G.f.: (1+x (45+x (8712+x (190668+x (982290+x (1543254+x (784080+x (116268+x (3477+5 x)))))))))/(x-1)^10 [From Harvey P. Dale, Mar 14 2011]
%e a(5) = 1 + 2*5 + 3*5^2 + 4*5^3 + 5*5^4 + 6*5^5 + 7*5^6 + 8*5^7 + 9*5^8 + 10*5^9 = 23803711 is prime.
%e a(30) = 1 + 2*30 + 3*30^2 + 4*30^3 + 5*30^4 + 6*30^5 + 7*30^6 + 8*30^7 + 9*30^8 + 10*30^9 = 202915112960761 is prime.
%t With[{eq=Total[Range[10](n^Range[0,9])]},Table[eq,{n,0,20}]] (* _Harvey P. Dale_, Mar 14 2011 *)
%Y Cf. A000012, A005408, A056109, A056578, A056579.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Jan 14 2006