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A206816
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Sum_{0<j<n} (n!-j!).
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4
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1, 9, 63, 447, 3447, 29367, 276327, 2856807, 32250087, 395130087, 5225062887, 74201293287, 1126567808487, 18213512883687, 312440245683687, 5668674457011687, 108462341176755687, 2182831421832627687, 46096712669420979687
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = n*n!-p(n), where p(n) is the n-th partial sum of (j!).
a(n) = t(n)-t(n-1), where t = A206817.
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EXAMPLE
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a(4) = (24-1) + (24-2) + (24-6) = 63.
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MATHEMATICA
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s[k_] := k!; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1];
Table[c[n], {n, 2, 32}] (* A206816 *)
Flatten[Table[t[n], {n, 2, 20}]] (* A206817 *)
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PROG
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(Sage) [sum([factorial(n)-factorial(j) for j in range(1, n)]) for n in range(2, 21)] # Danny Rorabaugh, Apr 18 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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