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%I #6 Feb 10 2024 11:59:36
%S 1,4,30,320,4550,82152,1808268,47018400,1410564870,47959254200,
%T 1822451844356,76542978168384,3520976998449820,176048849932891600,
%U 9506637896416263000,551384997992298371520,34185869875523100114630,2256267411784526941171800,157938718824916894957161300
%N a(n) = Sum_{j=0..n} (2*n)! / (n!*(n - j)!).
%F a(n) = (exp(1) * Gamma(n + 1, 1) * Gamma(2*n + 1)) / Gamma(n + 1)^2.
%F a(n) * n! = A367962(2*n, n).
%p a := n -> add((2*n)!/(n!*(n-j)!), j = 0..n):
%p seq(a(n), n = 0..18);
%t Table[Sum[(2n)!/(n!(n-j)!),{j,0,n}],{n,0,20}] (* _Harvey P. Dale_, Feb 10 2024 *)
%Y Cf. A367962.
%K nonn
%O 0,2
%A _Peter Luschny_, Dec 06 2023
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