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A206817
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Sum_{0<j<k<=n} (k!-j!).
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10
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1, 10, 73, 520, 3967, 33334, 309661, 3166468, 35416555, 430546642, 5655609529, 79856902816, 1206424711303, 19419937594990, 331860183278677, 6000534640290364, 114462875817046051, 2297294297649673738, 48394006967070653425
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OFFSET
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2,2
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COMMENTS
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In the following guide to related sequences,
c(n) = Sum_{0<j<n} s(n)-s(j),
t(n) = Sum_{0<j<k<=n} s(k)-s(j).
s(k).................c(n)........t(n)
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LINKS
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FORMULA
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a(n) = a(n-1)+(n-1)s(n)-p(n-1), where s(n) = n! and p(k) = 1!+2!+...+k!.
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EXAMPLE
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a(3) = (2-1) + (6-1) + (6-2) = 10.
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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([sum([factorial(k)-factorial(j) for j in range(1, k)]) for k in range(2, n+1)]) 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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