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 A053805 #31 Jul 09 2025 22:10:48
%S A053805 1,25,313,2625,16641,85305,369305,1392065,4673345,14218905,39753273,
%T A053805 103274625,251595969,579168825,1267854873,2653649025,5334940545,
%U A053805 10343052825,19403906105,35330137025,62596382081,108167252025,182668423833,302016962625,489658242241
%N A053805 Expansion of (1 + x)^12 / (1 - x)^13.
%C A053805 This is row/column 12 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - _Peter Munn_, Jan 05 2023
%H A053805 T. D. Noe, <a href="/A053805/b053805.txt">Table of n, a(n) for n = 0..1000</a>
%H A053805 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A053805 G.f.: (1+x)^12/(1-x)^13.
%F A053805 a(n) = A240876(n) + 2*Sum_{i=0..n-1} A240876(i) for n>0, a(0)=1. - _Bruno Berselli_, Apr 17 2014
%F A053805 a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13). - _Wesley Ivan Hurt_, Jul 09 2025
%t A053805 CoefficientList[Series[(1 + x)^12/(1 - x)^13, {x, 0, 30}], x] (* _Bruno Berselli_, Apr 17 2014 *)
%o A053805 (PARI) Vec((1+x)^12/(1-x)^13+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o A053805 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)^12/(1-x)^13)); // _Bruno Berselli_, Apr 17 2014
%Y A053805 Cf. A008288, A240876.
%K A053805 nonn,easy
%O A053805 0,2
%A A053805 _R. K. Guy_, Apr 07 2000