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 A081583 #22 Sep 08 2022 08:45:09
%S A081583 1,10,46,136,307,586,1000,1576,2341,3322,4546,6040,7831,9946,12412,
%T A081583 15256,18505,22186,26326,30952,36091,41770,48016,54856,62317,70426,
%U A081583 79210,88696,98911,109882,121636,134200,147601,161866,177022,193096
%N A081583 Third row of Pascal-(1,2,1) array A081577.
%C A081583 Equals binomial transform of [1, 9, 27, 27, 0, 0, 0, ...] where (1, 9, 27, 27) = row 3 of triangle A013610. - _Gary W. Adamson_, Jul 19 2008
%H A081583 Vincenzo Librandi, <a href="/A081583/b081583.txt">Table of n, a(n) for n = 0..1000</a>
%H A081583 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081583 a(n) = (2 + 9*n + 9*n^3)/2.
%F A081583 G.f.: (1+2*x)^3/(1-x)^4.
%F A081583 a(n) = hypergeommetric2F1([-n, -3], [1], 3). - _Peter Luschny_, Nov 19 2014
%F A081583 E.g.f.: (1/2)*(2 + 18*x + 27*x^2 + 9*x^3)*exp(x). - _G. C. Greubel_, May 25 2021
%p A081583 seq((2+9*n+9*n^3)/2, n=0..40); # _G. C. Greubel_, May 25 2021
%t A081583 CoefficientList[Series[(1+2x)^3/(1-x)^4, {x,0,50}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%t A081583 LinearRecurrence[{4,-6,4,-1},{1,10,46,136},60] (* _Harvey P. Dale_, Oct 01 2021 *)
%o A081583 (Magma) [(2+9*n+9*n^3)/2: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%o A081583 (Sage)
%o A081583 a = lambda n: hypergeometric([-n, -3], [1], 3)
%o A081583 [simplify(a(n)) for n in range(36)] # _Peter Luschny_, Nov 19 2014
%Y A081583 Cf. A013610, A038764, A081584, A081577.
%K A081583 easy,nonn
%O A081583 0,2
%A A081583 _Paul Barry_, Mar 23 2003