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%I #15 Mar 15 2017 15:43:28
%S 1,21,321,2005,7737,22461,54121,114381,219345,390277,654321,1045221,
%T 1604041,2379885,3430617,4823581,6636321,8957301,11886625,15536757,
%U 20033241,25515421,32137161,40067565,49491697,60611301,73645521
%N a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5.
%C 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 = (n^7 - 1)/(n-1). a(6) = 1 + 2*6 + 3*6^2 + 4*6^3 + 5*6^4 + 6*6^5 = 54121 is prime, the smallest prime in the sequence. The next is a(a(1)) = a(21) = 1 + 2*21 + 3*21^2 + 4*21^3 + 5*21^4 + 6*21^5 = 25515421. Then a(24) = 49491697.
%H G. C. Greubel, <a href="/A113531/b113531.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5.
%F O.g.f.: 2064/(-1+x)^4+3/(-1+x)+2040/(-1+x)^5+132/(-1+x)^2+720/(-1+x)^6+872/(-1+x)^3 . - _R. J. Mathar_, Feb 26 2008
%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), a(0)=1, a(1)=21, a(2)=321, a(3)=2005, a(4)=7737, a(5)=22461. - _Harvey P. Dale_, Nov 02 2011
%t With[{eq=Total[# n^(#-1)&/@Range[6]]},Table[eq,{n,0,30}]] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,21,321,2005,7737,22461},30] (* _Harvey P. Dale_, Nov 02 2011 *)
%o (PARI) for(n=0,50, print1(1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5, ", ")) \\ _G. C. Greubel_, Mar 15 2017
%Y Cf. A000012, A005408, A056109, A056578, A056579.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Jan 12 2006
%E Corrected by _R. J. Mathar_, Feb 26 2008
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