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 A143131 #14 Aug 18 2025 00:07:40
%S A143131 1,5,19,63,157,321,575,939,1433,2077,2891,3895,5109,6553,8247,10211,
%T A143131 12465,15029,17923,21167,24781,28785,33199,38043,43337,49101,55355,
%U A143131 62119,69413,77257,85671,94675,104289,114533,125427,136991,149245
%N A143131 Binomial transform of [1, 4, 10, 20, 0, 0, 0, ...].
%H A143131 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A143131 Binomial transform of [1, 4, 10, 20, 0, 0, 0, ...], where (1, 4, 10, 20) = row 3 of triangle A046899
%F A143131 a(n) = (-39 + 77*n - 45*n^2 + 10*n^3)/3. - _T. D. Noe_, Aug 22 2008
%F A143131 G.f.: x*(1+x+5*x^2+13*x^3)/(1-x)^4. - _Colin Barker_, Mar 23 2012
%e A143131 a(4) = 63 = (1, 3, 3, 1) dot (1, 4, 10, 20) = (1 + 12 + 30 + 20).
%t A143131 LinearRecurrence[{4,-6,4,-1},{1,5,19,63},37] (* or *) Rest[CoefficientList[Series[x*(1+x+5*x^2+13*x^3)/(1-x)^4,{x,0,37}],x]] (* or *) a[n_]:=(-39 + 77*n - 45*n^2 + 10*n^3)/3;Array[a,37] (* _James C. McMahon_, Aug 17 2025 *)
%Y A143131 Cf. A046899.
%K A143131 nonn,easy
%O A143131 1,2
%A A143131 _Gary W. Adamson_, Jul 27 2008
%E A143131 More terms from _T. D. Noe_, Aug 22 2008