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A206817
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Sum{k!-j! : 0<j<k<n}.
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9
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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{s(n)-s(j) : 0<j<n},
t(n)=sum{s(k)-s(j) : 0<j<k<n}.
s(k).................c(n)........t(n)
k....................A000217.....A000292
k^2..................A016061.....A004320
k^3..................A206808.....A206809
k^4..................A206810.....A206811
k!...................A206816.....A206817
prime(k).............A152535.....A062020
prime(k+1)...........A185382.....A206803
2^(k-1)..............A000337.....A045618
k(k+1)/2.............A007290.....A034827
k-th quarter-square..A049774.....A206806
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LINKS
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Table of n, a(n) for n=2..20.
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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!; also, a(n) = n-th partial sum of A206816.
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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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CROSSREFS
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Cf. A000142, A206816.
Sequence in context: A055424 A200580 A181678 * A159687 A199556 A044197
Adjacent sequences: A206814 A206815 A206816 * A206818 A206819 A206820
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Feb 12 2012
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STATUS
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approved
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