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Search: id:A125598
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| A125598 |
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Quotient ((n+1)^(n-1)-1)/n. |
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+0
2
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| 0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Odd prime p divides a(p-2). (2k+1) divides a(2k-1) for k>0. a(2k-1)/(2k+1) = {0,1,37,4161,1010101,432988561,290738012181,282578800148737,...} = A125599(k). a(n) is prime for n = {3,4,6,74,...}. Prime a(n) are {5,31,2801,1023859838465486686363016033998704522272171328793086532353874352382193497640442165979330173110543821617750919555161286749549814172693201,...}.
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FORMULA
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a(n) = ((n+1)^(n-1)-1)/n. a(n) = (A000272[n+1]-1)/n.
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MAPLE
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a:=n->sum ((n+3)^j, j=0..n): seq(a(n), n=-1..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2008]
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MATHEMATICA
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Table[((n+1)^(n-1)-1)/n, {n, 1, 25}]
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 1, n+2) for n in xrange(0, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
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CROSSREFS
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Cf. A125599 = ((2n)^(2n-2)-1)/(2n+1)/(2n-1). Cf. A000272 = n^(n-2).
Sequence in context: A126121 A167137 A000556 this_sequence A058892 A056187 A056790
Adjacent sequences: A125595 A125596 A125597 this_sequence A125599 A125600 A125601
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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), Nov 26 2006
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