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A062024
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a(n) = ((n+1)^n + (n-1)^n)/2.
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10
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1, 1, 5, 36, 353, 4400, 66637, 1188544, 24405761, 567108864, 14712104501, 421504185344, 13218256749601, 450353989316608, 16565151205544957, 654244800082329600, 27614800115689879553, 1240529732459024678912, 59095217374989483261925, 2975557672677668838178816
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OFFSET
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0,3
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COMMENTS
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Let b(n) = A302583(n) = ((n+1)^n - (n-1)^n)/2 = 0, 1, 4, 28, 272, ... then lim_{n -> infinity} b(n)/a(n) = tanh(1) = 0.76159415... . - Thomas Ordowski, Dec 06 2012
Obviously, a(n) is always odd number for even n. - Altug Alkan, Sep 28 2015
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LINKS
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FORMULA
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EXAMPLE
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a(3) = (4^3 + 2^3)/2 = 36.
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MAPLE
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MATHEMATICA
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PROG
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(PARI) { for (n=0, 100, write("b062024.txt", n, " ", ((n + 1)^n + (n - 1)^n)/2) ) } \\ Harry J. Smith, Jul 29 2009
(Sage) [((n+1)^n + (n-1)^n)/2 for n in (0..20)] # G. C. Greubel, Jan 03 2020
(GAP) List([0..20], n-> ((n+1)^n + (n-1)^n)/2); # G. C. Greubel, Jan 03 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, Jun 06 2001
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STATUS
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approved
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