%I #29 Aug 13 2024 04:15:28
%S 1,25,313,2625,16641,85305,369305,1392065,4673345,14218905,39753273,
%T 103274625,251595969,579168825,1267854873,2653649025,5334940545,
%U 10343052825,19403906105,35330137025,62596382081,108167252025,182668423833,302016962625,489658242241
%N Expansion of (1 + x)^12 / (1 - x)^13.
%C 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 T. D. Noe, <a href="/A053805/b053805.txt">Table of n, a(n) for n = 0..1000</a>
%H <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 G.f.: (1+x)^12/(1-x)^13.
%F a(n) = A240876(n) + 2*sum( A240876(i), i=0..n-1 ) for n>0, a(0)=1. - _Bruno Berselli_, Apr 17 2014
%t CoefficientList[Series[(1 + x)^12/(1 - x)^13, {x, 0, 30}], x] (* _Bruno Berselli_, Apr 17 2014 *)
%o (PARI) Vec((1+x)^12/(1-x)^13+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)^12/(1-x)^13)); // _Bruno Berselli_, Apr 17 2014
%Y Cf. A008288, A240876.
%K nonn,easy
%O 0,2
%A _R. K. Guy_, Apr 07 2000