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Search: id:A120485
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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
1
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| 1, 3, 20, 190, 2313, 34461, 607408, 12360636, 285188825, 7356173275, 209762134236, 6552069616170, 222481706868337, 8159714626124985, 321456928026650816, 13538204870285608696, 606979028986115413329
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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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
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Table[Sum[(-1)^(k+n)*k^n, {k, 1, n}], {n, 1, 25}]
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CROSSREFS
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Cf. A031971.
Adjacent sequences: A120482 A120483 A120484 this_sequence A120486 A120487 A120488
Sequence in context: A065980 A073767 A108206 this_sequence A087152 A054361 A052595
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 22 2006
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