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 A144513 #15 Apr 08 2019 03:44:22
%S A144513 2,18,162,1670,19980,274932,4296278,75324762,1466031690,31386435410,
%T A144513 733391707752,18578222154648,507246285802802,14851746921266010,
%U A144513 464244744007818090,15431886798641124662,543593886328031841828,20228083875146926867932,792934721766833544369830
%N A144513 a(n) = Sum_{k=0..n} (n+k+2)!/((n-k)!*k!*2^k).
%H A144513 Seiichi Manyama, <a href="/A144513/b144513.txt">Table of n, a(n) for n = 0..402</a>
%F A144513 n^2*a(n) = (2*n+1)*(n^2+n+1)*a(n-1) + (n+1)^2*a(n-2). - _Seiichi Manyama_, Apr 07 2019
%p A144513 f2:=proc(n) local k; add((n+k+2)!/((n-k)!*k!*2^k),k=0..n); end; [seq(f2(n),n=0..50)];
%o A144513 (PARI) {a(n) = sum(k=0, n, (n+k+2)!/((n-k)!*k!*2^k))} \\ _Seiichi Manyama_, Apr 07 2019
%Y A144513 Equals 2*A001514 (with a different offset).
%Y A144513 Cf. A001515, A144498, A144514.
%K A144513 nonn
%O A144513 0,1
%A A144513 _N. J. A. Sloane_, Dec 16 2008