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 A102909 #58 Feb 01 2025 13:29:51
%S A102909 1,9,511,9841,87381,488281,2015539,6725601,19173961,48427561,
%T A102909 111111111,235794769,469070941,883708281,1589311291,2745954241,
%U A102909 4581298449,7411742281,11668193551,17927094321,26947368421,39714002329,57489010371,81870575521,114861197401
%N A102909 a(n) = Sum_{j=0..8} n^j.
%H A102909 G. C. Greubel, <a href="/A102909/b102909.txt">Table of n, a(n) for n = 0..1000</a>
%H A102909 Carlos M. da Fonseca and Anthony G. Shannon, <a href="https://doi.org/10.7546/nntdm.2024.30.3.491-498">A formal operator involving Fermatian numbers</a>, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
%H A102909 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A102909 a(n) = (n^2+n+1) * (n^6+n^3+1) and so is never prime. - _Jonathan Vos Post_, Dec 21 2012
%F A102909 G.f.: (x^8 + 162*x^7 + 3418*x^6 + 14212*x^5 + 16578*x^4 + 5482*x^3 + 466*x^2 + 1)/(1-x)^9. - _Colin Barker_, Nov 05 2012, edited by _M. F. Hasler_, Dec 31 2012
%F A102909 a(n) = (n^9-1)/(n-1) with a(1) = 9. - _L. Edson Jeffery_ and _M. F. Hasler_, Dec 30 2012
%F A102909 E.g.f.: exp(x)*(1 + 8*x + 247*x^2 + 1389*x^3 + 2127*x^4 + 1206*x^5 + 288*x^6 + 29*x^7 + x^8). - _Stefano Spezia_, Oct 03 2024
%t A102909 1 + Sum[Range[0, 30]^j, {j, 1, 8}] (* _G. C. Greubel_, Feb 13 2018 *)
%t A102909 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,9,511,9841,87381,488281,2015539,6725601,19173961},30] (* _Harvey P. Dale_, Feb 01 2025 *)
%o A102909 (PARI) a(n)=n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A102909 (Magma) [(&+[n^j: j in [0..8]]): n in [0..30]]; // _G. C. Greubel_, Feb 13 2018
%o A102909 (Sage) [sum(n^j for j in (0..8)) for n in (0..30)] # _G. C. Greubel_, Apr 14 2019
%Y A102909 Cf. A001016, A060890, A059839.
%Y A102909 Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), this sequence (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).
%K A102909 nonn,easy
%O A102909 0,2
%A A102909 Douglas Winston (douglas.winston(AT)srupc.com), Mar 01 2005
%E A102909 Offset corrected by _N. J. A. Sloane_, Dec 30 2012