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