%I #10 Jan 09 2024 12:38:53
%S 1,4,33,496,11905,416676,20000449,1260028288,100802263041,
%T 9979424041060,1197530884927201,171246916544589744,
%U 28769481979491076993,5610048986000760013636,1256650972864170243054465,320445998080363411978888576
%N a(n) = n! * (n+2)! * Sum_{k=0..n} 1/(k! * (k+2)!).
%F a(n) = n*(n+2)*a(n-1) + 1.
%F a(n) ~ BesselI(2,2) * n! * (n+2)!. - _Vaclav Kotesovec_, Jan 09 2024
%o (PARI) a(n) = n!*(n+2)!*sum(k=0, n, 1/(k!*(k+2)!));
%Y Cf. A099597, A006040, A228229, A368838.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jan 07 2024