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Sum_{0<j<n} (n!-j!).
4

%I #10 Apr 19 2015 00:19:56

%S 1,9,63,447,3447,29367,276327,2856807,32250087,395130087,5225062887,

%T 74201293287,1126567808487,18213512883687,312440245683687,

%U 5668674457011687,108462341176755687,2182831421832627687,46096712669420979687

%N Sum_{0<j<n} (n!-j!).

%H Danny Rorabaugh, <a href="/A206816/b206816.txt">Table of n, a(n) for n = 2..400</a>

%F a(n) = n*n!-p(n), where p(n) is the n-th partial sum of (j!).

%F a(n) = t(n)-t(n-1), where t = A206817.

%e a(4) = (24-1) + (24-2) + (24-6) = 63.

%t s[k_] := k!; t[1] = 0;

%t p[n_] := Sum[s[k], {k, 1, n}];

%t c[n_] := n*s[n] - p[n];

%t t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1];

%t Table[c[n], {n, 2, 32}] (* A206816 *)

%t Flatten[Table[t[n], {n, 2, 20}]] (* A206817 *)

%o (Sage) [sum([factorial(n)-factorial(j) for j in range(1,n)]) for n in range(2,21)] # _Danny Rorabaugh_, Apr 18 2015

%Y Cf. A000142, A206817.

%K nonn

%O 2,2

%A _Clark Kimberling_, Feb 12 2012