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a(n) = Sum{0<=k<=n} binomial(n+k, n-k) * k! / (floor(k/2)! * floor((k+2)/2)!).
2

%I #7 Mar 28 2020 06:09:01

%S 1,2,5,15,49,163,549,1875,6477,22571,79213,279631,991985,3533707,

%T 12632909,45301795,162890781,587091795,2120442517,7672891151,

%U 27811187377,100956896179,366983328885,1335662387699

%N a(n) = Sum{0<=k<=n} binomial(n+k, n-k) * k! / (floor(k/2)! * floor((k+2)/2)!).

%C Row sums of A190907.

%p A190908 := n -> add(binomial(n+k,n-k)*k!/(iquo(k,2)!*iquo(k+2,2)!), k=0..n): seq(A190908(n), n=0..24);

%K nonn

%O 0,2

%A _Peter Luschny_, May 24 2011