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 A052161 #23 Sep 08 2022 08:44:59
%S A052161 1,7,34,146,599,2417,9696,38820,155325,621355,2485486,9942022,
%T A052161 39768179,159072821,636291404,2545165752,10180663161,40722652815,
%U A052161 162890611450,651562446010
%N A052161 Partial sums of A014825, second partial sums of A002450.
%D A052161 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A052161 Vincenzo Librandi, <a href="/A052161/b052161.txt">Table of n, a(n) for n = 0..1000</a>
%H A052161 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,13,-4)
%F A052161 a(n) = ((2^(2n+7)) - (9*(n^2) + 51n + 74))/54.
%F A052161 a(n) = 4a(n-1) + C(n+2,2); a(0)=1.
%F A052161 a(n) = Sum_{k=0..n, binomial(n+3, k+3)3^k}. - _Paul Barry_, Aug 20 2004
%F A052161 G.f.: 1/((1-x)^3*(1-4*x)). - _Colin Barker_, Jan 12 2012
%t A052161 CoefficientList[Series[1/((1-x)^3*(1-4*x)),{x,0,25}],x] (* _Vincenzo Librandi_, Apr 28 2012 *)
%o A052161 (Magma) [((2^(2*n+7))-(9*(n^2)+51*n+74))/54: n in [0..25]]; // _Vincenzo Librandi_, Apr 28 2012
%Y A052161 Cf. A014825, A002450, A000302.
%K A052161 easy,nonn
%O A052161 0,2
%A A052161 _Barry E. Williams_, Jan 25 2000