%I #31 Feb 20 2024 11:17:18

%S 1,0,0,2,14,86,566,4166,34406,316646,3219686,35878886,435046886,

%T 5704064486,80428314086,1213746099686,19521187251686,333363035571686,

%U 6024361885107686,114864714882483686,2304476522241459686

%N a(n) = n! - Sum_{k=0..n-1} k!.

%C For n > 1, the factorial base representation of a(n) is {n-2, n-3, ..., 1, 0}, i.e., the numbers 0..(n-2) in descending order. - _Amiram Eldar_, Apr 24 2021

%H Harry J. Smith, <a href="/A065355/b065355.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = A000142(n) - A003422(n). - _Darío Clavijo_, Feb 16 2024

%t Table[ n! - Sum[k!, {k, 0, n - 1} ], {n, 0, 20} ]

%o (PARI) a(n) = n! - sum(k=0, n-1, k!); \\ _Harry J. Smith_, Oct 17 2009

%o (Python)

%o from sympy import factorial

%o left_factorial = lambda n: left_factorial(n - 1) + factorial(n - 1) if n > 0 else 0

%o a = lambda n: factorial(n) - left_factorial(n) # _Darío Clavijo_, Feb 16 2024

%Y Cf. A000142, A003422, A007623.

%K easy,nonn

%O 0,4

%A _Floor van Lamoen_, Oct 31 2001