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A120485
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n^n - (n-1)^n + (n-2)^n - ... + (-1)^(k+n)*k^n + ... + (-1)^(2+n)*2^n + (-1)^(1+n)*1^n = Sum[(-1)^(k+n)*k^n,{k,1,n}].
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0
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1, 3, 20, 190, 2313, 34461, 607408, 12360636, 285188825, 7356173275, 209762134236, 6552069616170, 222481706868337, 8159714626124985, 321456928026650816, 13538204870285608696, 606979028986115413329
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| p divides a(p-1) for prime p>2. p^k divides a(p^k-1) for all prime p and integer k>1. p^2 divides a(2p) and a(2p-1) for prime p>2. (p^k)^2 divides a(2p^k) for prime p>2 and integer k>0. (p^k)^2 divides a(2p^k-1) for all prime p and integer k>1.
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FORMULA
| a(n) = Sum[(-1)^(k+n)*k^n,{k,1,n}]. a(n) = (-1)^n*((-1+2^(n+1))*Zeta[ -n] + (-2)^n*((Zeta[ -n,(n+1)/2] - Zeta[ -n,(n+2)/2]))).
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MATHEMATICA
| Table[Sum[(-1)^(k+n)*k^n, {k, 1, n}], {n, 1, 25}]
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CROSSREFS
| Cf. A031971.
Sequence in context: A073767 A176043 A108206 * A087152 A158833 A054361
Adjacent sequences: A120482 A120483 A120484 * A120486 A120487 A120488
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 22 2006
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