This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355510 #36 Oct 29 2022 11:12:42
%S A355510 0,0,21,112,819,5712,39991,279936,1959552,13716864,96018048,672126336,
%T A355510 4704884352,32934190464,230539333248,1613775332736,11296427329152,
%U A355510 79074991304064,553524939128448,3874674573899136,27122722017293952
%N A355510 a(n) is the number of monic polynomials of degree n over GF(7) without linear factors.
%H A355510 A. Knopfmacher and J. Knopfmacher, <a href="https://doi.org/10.1016/0012-365X(93)90227-K">Counting irreducible factors of polynomials over a finite field</a>, Discrete Mathematics, Volume 112, Issues 1-3, 1993, Pages 103-118.
%H A355510 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (7).
%F A355510 O.g.f.: (1 - z)^7/(1 - 7*z) - 1.
%F A355510 For n >= 7, a(n) = 6^7 * 7^(n-7).
%e A355510 a(0) = 0 since all constant polynomials are units (as GF(7) is a field).
%e A355510 a(1) = 0 since all polynomials of degree 1 have linear factors.
%e A355510 a(2), the number of quadratic polynomials without linear factors, then coincides with the number of irreducible quadratics in GF(7), which is known to be M(7,2), where M(a,d) is the necklace polynomial, so a(2) = 21.
%t A355510 CoefficientList[Series[(1-z)^7/(1-7 z)-1,{z,0,15}]//Normal,z] (* For all terms *)
%t A355510 (7^(#-7)) &/@ Range[7,15]*6^7 (* For n>=7 *)
%t A355510 Join[{0,0,21,112,819,5712,39991},NestList[7#&,279936,20]] (* _Harvey P. Dale_, Oct 29 2022 *)
%K A355510 nonn,easy
%O A355510 0,3
%A A355510 _Greyson C. Wesley_, Jul 04 2022