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 A195160 #53 Nov 21 2024 19:24:42
%S A195160 0,1,8,11,25,30,51,58,86,95,130,141,183,196,245,260,316,333,396,415,
%T A195160 485,506,583,606,690,715,806,833,931,960,1065,1096,1208,1241,1360,
%U A195160 1395,1521,1558,1691,1730,1870,1911,2058,2101,2255,2300,2461,2508,2676
%N A195160 Generalized 11-gonal (or hendecagonal) numbers: m*(9*m - 7)/2 with m = 0, 1, -1, 2, -2, 3, -3, ...
%C A195160 Exponents of q in the expansion of Product_{n >= 1} (1 - q^(9*n))*(1 + q^(9*n-1))*(1 + q^(9*n-8)) = 1 + q + q^8 + q^11 + q^25 + q^30 + .... - _Peter Bala_, Nov 21 2024
%H A195160 Vincenzo Librandi, <a href="/A195160/b195160.txt">Table of n, a(n) for n = 0..1000</a>
%H A195160 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A195160 From _Bruno Berselli_, Sep 14 2011: (Start)
%F A195160 G.f.: x*(1+7*x+x^2)/((1+x)^2*(1-x)^3).
%F A195160 a(n) = (18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16.
%F A195160 a(2n) = A062728(n), a(2n-1) = A051682(n). (End)
%F A195160 Sum_{n>=1} 1/a(n) = 18/49 + 2*Pi*cot(2*Pi/9)/7. - _Vaclav Kotesovec_, Oct 05 2016
%t A195160 CoefficientList[Series[x (1 + 7 x + x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 60}], x] (* _Vincenzo Librandi_, Apr 09 2013 *)
%o A195160 (Magma) I:=[0, 1, 8, 11, 25]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Apr 09 2013
%o A195160 (PARI) a(n)=(18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A195160 Partial sums of A195159.
%Y A195160 Column 7 of A195152.
%Y A195160 Cf. A316672.
%Y A195160 Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), this sequence (k=11), A195162 (k=12), A195313 (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).
%K A195160 nonn,easy
%O A195160 0,3
%A A195160 _Omar E. Pol_, Sep 10 2011