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a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4.
6

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

%S 1,10,97,424,1249,2926,5905,10732,18049,28594,43201,62800,88417,

%T 121174,162289,213076,274945,349402,438049,542584,664801,806590,

%U 969937,1156924,1369729,1610626,1881985,2186272,2526049,2903974,3322801,3785380

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

%C The subsequence of primes begins: 97, 1249, 18049, 43201, 162289, 438049, 2526049, a(32) = 4294657, a(44) = 15251809, a(48) = 21570049.

%H G. C. Greubel, <a href="/A209262/b209262.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: (4*x^4+29*x^3+57*x^2+5*x+1) / (1-x)^5. - _Colin Barker_, Jan 26 2013

%e a(4) = 1 + 2*4^2 + 3*4^3 + 4*4^4 = 1249.

%t Table[Sum[k*n^k, {k,2,4}], {n,0,30}] (* _G. C. Greubel_, Jan 05 2018 *)

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

%o (PARI) a(n)=1+2*n^2+3*n^3+4*n^4 \\ _Charles R Greathouse IV_, Oct 07 2015

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

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, Jan 14 2013