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A266229 a(n) = Sum_{j=0..12} (-n)^j.

%I A266229 #24 Mar 11 2025 11:41:09
%S A266229 1,1,2731,398581,13421773,203450521,1865813431,12111126301,
%T A266229 61083979321,254186582833,909090909091,2876892678661,8230246567621,
%U A266229 21633936185161,52914318216943,121637191772461,264917625139441,550254335161441
%N A266229 a(n) = Sum_{j=0..12} (-n)^j.
%C A266229 a(n) = Phi_26(n) where Phi_k(x) is the k-th cyclotomic polynomial.
%H A266229 G. C. Greubel, <a href="/A266229/b266229.txt">Table of n, a(n) for n = 0..1000</a>
%H A266229 OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>
%H A266229 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H A266229 <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%H A266229 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
%F A266229 G.f.: (1 - 12*x + 2796*x^2 + 362870*x^3 + 8453667*x^4 + 59275152*x^5 + 155813880*x^6 + 167535876*x^7 + 74215935*x^8 + 12641708*x^9 + 691692*x^10 + 8022*x^11 + 13*x^12)/(1 - x)^13.
%F A266229 Sum_{n>=0} 1/a(n) = 2.0003687552...
%t A266229 Table[n^12-n^11+n^10-n^9+n^8-n^7+n^6-n^5+n^4-n^3+n^2-n+1, {n, 0, 17}]
%t A266229 Table[Cyclotomic[26, n], {n, 0, 17}]
%o A266229 (PARI) a(n) = polcyclo(26, n); \\ _Michel Marcus_, Mar 13 2016
%o A266229 (Magma) [(&+[(-n)^j: j in [0..12]]): n in [0..20]]; // _G. C. Greubel_, Apr 24 2019
%o A266229 (Sage) [sum((-n)^j for j in (0..12)) for n in (0..20)] # _G. C. Greubel_, Apr 24 2019
%o A266229 (GAP) List([0..20], n-> Sum([0..12], j-> (-n)^j)); # _G. C. Greubel_, Apr 24 2019
%Y A266229 Cf. similar sequences of the type Phi_k(n) listed in A269442.
%K A266229 nonn,easy
%O A266229 0,3
%A A266229 _Ilya Gutkovskiy_, Mar 13 2016
%E A266229 Name changed by _G. C. Greubel_, Apr 24 2019