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A076809 a(n) = n^4 + 853n^3 + 2636n^2 + 3536n + 1753.

%I A076809 #31 Feb 16 2025 08:32:47
%S A076809 1753,8779,26209,59197,112921,192583,303409,450649,639577,875491,
%T A076809 1163713,1509589,1918489,2395807,2946961,3577393,4292569,5097979,
%U A076809 5999137,7001581,8110873,9332599,10672369,12135817,13728601,15456403,17324929,19339909,21507097,23832271,26321233,28979809,31813849,34829227
%N A076809 a(n) = n^4 + 853n^3 + 2636n^2 + 3536n + 1753.
%C A076809 A prime-generating quartic polynomial.
%C A076809 For n=0 ... 20, the terms in this sequence are primes.  This is not the case for n=21. See A272325 and A272326. - _Robert Price_, Apr 25 2016
%H A076809 Harvey P. Dale, <a href="/A076809/b076809.txt">Table of n, a(n) for n = 0..1000</a>
%H A076809 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a>
%H A076809 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A076809 G.f.: -(x^4-1588*x^3-156*x^2+14*x+1753)/(x- 1)^5. [_Colin Barker_, Nov 11 2012]
%F A076809 E.g.f.: (1753 + 7026*x + 5202*x^2 + 859*x^3 + x^4)*exp(x). - _Ilya Gutkovskiy_, Apr 25 2016
%p A076809 A076809:=n->n^4 + 853*n^3 + 2636*n^2 + 3536*n + 1753; seq(A076809(n), n=0..100); # _Wesley Ivan Hurt_, Nov 13 2013
%t A076809 Table[n^4 + 853n^3 + 2636n^2 + 3536n + 1753, {n,0,100}] (* _Wesley Ivan Hurt_, Nov 13 2013 *)
%t A076809 CoefficientList[Series[-(x^4 - 1588 x^3 - 156 x^2 + 14 x + 1753)/(x - 1)^5, {x, 0, 33}], x] (* _Michael De Vlieger_, Apr 25 2016 *)
%t A076809 LinearRecurrence[{5,-10,10,-5,1},{1753,8779,26209,59197,112921},40] (* _Harvey P. Dale_, Jan 20 2025 *)
%o A076809 (Maxima) A076809(n):=n^4 + 853*n^3 + 2636*n^2 + 3536*n + 1753$
%o A076809 makelist(A076809(n),n,0,30); /* _Martin Ettl_, Nov 08 2012 */
%Y A076809 Cf. A076808, A272325, A272326.
%K A076809 easy,nonn
%O A076809 0,1
%A A076809 Hilko Koning (hilko(AT)hilko.net), Nov 18 2002
%E A076809 More terms from _Michael De Vlieger_, Apr 25 2016