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a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5.
5

%I #25 Sep 08 2022 08:46:01

%S 1,15,257,1639,6369,18551,44785,94767,181889,323839,543201,868055,

%T 1332577,1977639,2851409,4009951,5517825,7448687,9885889,12923079,

%U 16664801,21227095,26738097,33338639,41182849,50438751,61288865,73930807,88577889,105459719

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

%C This is to 5 as A209262 1 + 2*n^2 + 3*n^3 + 4*n^4 is to 4. The subsequence of primes begins: 257, 181889, 7448687, 16664801, a(60) = 3940495201.

%H G. C. Greubel, <a href="/A209263/b209263.txt">Table of n, a(n) for n = 0..5000</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 G.f. ( 1+9*x+182*x^2+302*x^3+105*x^4+x^5 ) / (x-1)^6 . - _R. J. Mathar_, Jan 17 2013

%e a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 + 5*2^5 = 257.

%t With[{c=1+Total[Table[k n^k,{k,2,5}]]},Table[c,{n,0,30}]] (* _Harvey P. Dale_, Aug 01 2016 *)

%o (Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5,n,0,20); /* _Martin Ettl_, Jan 15 2013*/

%o (PARI) a(n)=1+2*n^2+3*n^3+4*n^4+5*n^5 \\ _Charles R Greathouse IV_, Oct 16 2015

%o (Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5: n in [0..30]]; // _G. C. Greubel_, Jan 04 2018

%Y Cf. A209262.

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, Jan 14 2013