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 A146983 #17 Sep 08 2022 08:45:38
%S A146983 1,2,10,35,133,494,1846,6887,25705,95930,358018,1336139,4986541,
%T A146983 18610022,69453550,259204175,967363153,3610248434,13473630586,
%U A146983 50284273907,187663465045,700369586270,2613814880038,9754889933879,36405744855481,135868089488042
%N A146983 a(n) = A002531(n)*A002531(n+1).
%C A146983 a(n+1) is the Hankel transform of A051960 aerated.
%H A146983 G. C. Greubel, <a href="/A146983/b146983.txt">Table of n, a(n) for n = 0..1000</a>
%H A146983 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-1).
%F A146983 From _Peter Bala_, May 01 2012: (Start)
%F A146983 a(n) = (-1)^n + 3*Sum_{k = 1..n} (-1)^(n-k)*6^(k-1)*binomial(n+k,2*k).
%F A146983 a(n) = (-1)^n*R(n,-3), where R(n,x) is the n-th row polynomial of A211955.
%F A146983 a(n) = (-1)^n*1/u*T(n,u)*T(n+1,u) with u = sqrt(-1/2) and T(n,x) denotes the Chebyshev polynomial of the first kind Cf. A182432.
%F A146983 Recurrence: a(n) = 4*a(n-1) -a(n-2) +3*(-1)^n, with a(0) = 1 and a(1) = 2; a(n)*a(n-2) = a(n-1)*(a(n-1)+3*(-1)^n).
%F A146983 Sum_{k>=0} (-1)^k/a(k) = 1/sqrt(3). (End)
%F A146983 From _Colin Barker_, Jul 29 2013: (Start)
%F A146983 a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3).
%F A146983 G.f.: (1-x+x^2)/((1+x)*(1-4*x+x^2)). (End)
%p A146983 seq(coeff(series((1-x+x^2)/((1+x)*(1-4*x+x^2)), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Jan 09 2020
%t A146983 LinearRecurrence[{3,3,-1}, {1,2,10}, 30] (* _G. C. Greubel_, Jan 09 2020 *)
%o A146983 (PARI) my(x='x+O('x^30)); Vec((1-x+x^2)/((1+x)*(1-4*x+x^2))) \\ _G. C. Greubel_, Jan 09 2020
%o A146983 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x+x^2)/((1+x)*(1-4*x+x^2)) )); // _G. C. Greubel_, Jan 09 2020
%o A146983 (Sage)
%o A146983 def A146983_list(prec):
%o A146983 P.<x> = PowerSeriesRing(ZZ, prec)
%o A146983 return P( (1-x+x^2)/((1+x)*(1-4*x+x^2)) ).list()
%o A146983 A146983_list(30) # _G. C. Greubel_, Jan 09 2020
%o A146983 (GAP) a:=[1,2,10];; for n in [4..30] do a[n]:=3*a[n-1]+3*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jan 09 2020
%Y A146983 Cf. A001654, A182432, A211955.
%K A146983 easy,nonn
%O A146983 0,2
%A A146983 _Paul Barry_, Nov 04 2008
%E A146983 More terms from _Colin Barker_, Jul 29 2013