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A125598
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Quotient ((n+1)^(n-1)-1)/n.
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1
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0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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
| a(n) = ((n+1)^(n-1)-1)/n. a(n) = (A000272[n+1]-1)/n.
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MAPLE
| 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
| Table[((n+1)^(n-1)-1)/n, {n, 1, 25}]
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PROG
| (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
| Cf. A125599 = ((2n)^(2n-2)-1)/(2n+1)/(2n-1). Cf. A000272 = n^(n-2).
Sequence in context: A126121 A167137 A000556 * A058892 A177453 A176302
Adjacent sequences: A125595 A125596 A125597 * A125599 A125600 A125601
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 26 2006
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