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a(n) = n! - 2(n-1)! + 3(n-2)!.
2

%I #6 Jul 30 2024 05:15:28

%S 3,5,18,90,552,3960,32400,297360,3024000,33747840,410054400,

%T 5388768000,76161254400,1151998848000,18568976025600,317764871424000,

%U 5753767219200000,109907415281664000,2208818928476160000,46590073456582656000,1029117549458718720000

%N a(n) = n! - 2(n-1)! + 3(n-2)!.

%F D-finite with recurrence a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +3*(-n+4)*a(n-3)=0. - _R. J. Mathar_, Jul 30 2024

%p A374649 := proc(n)

%p n!-2*(n-1)!+3*(n-2)! ;

%p end proc:

%p seq(A374649(n),n=2..50) ; # _R. J. Mathar_, Jul 30 2024

%t Table[n! - 2 (n - 1)! + 3 (n - 2)!, {n, 2, 25}]

%Y Cf. A000142, A374650.

%K nonn

%O 2,1

%A _Clark Kimberling_, Jul 25 2024