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%I #6 Jan 06 2024 09:22:20
%S 0,1,7,85,1701,51031,2143303,120024969,8641797769,777761799211,
%T 85553797913211,11293101324543853,1761723806628841069,
%U 320633732806449074559,67333083889354305657391,16159940133445033357773841,4395503716297049073314484753
%N a(n) = (n+1) * (n!)^2 * Sum_{k=1..n} 1/((k+1) * (k!)^2).
%F a(0) = 0; a(n) = (n+1) * n * a(n-1) + 1.
%F a(n) = A228229(n) - (n+1) * (n!)^2.
%o (PARI) a(n) = (n+1)*n!^2*sum(k=1, n, 1/((k+1)*k!^2));
%Y Cf. A010790, A066998, A228229.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jan 05 2024