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A125598 a(n) = ((n+1)^(n-1)-1)/n. 1
0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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, 102385983846548668636301603399870452227217132879308653235387435238219349\

  7640442165979330173110543821617750919555161286749549814172693201, ...}.

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = ((n+1)^(n-1)-1)/n. a(n) = (A000272(n+1)-1)/n.

MAPLE

a:=n->sum ((n+3)^j, j=0..n): seq(a(n), n=-1..17); # Zerinvary Lajos, Dec 17 2008

MATHEMATICA

Table[((n+1)^(n-1)-1)/n, {n, 1, 25}]

PROG

(Sage) [gaussian_binomial(n, 1, n+2) for n in xrange(0, 18)] # Zerinvary Lajos, May 31 2009

CROSSREFS

Cf. A125599 = ((2n)^(2n-2)-1)/(2n+1)/(2n-1). Cf. A000272 = n^(n-2).

Sequence in context: A279434 A000556 A320512 * A267436 A294215 A294216

Adjacent sequences:  A125595 A125596 A125597 * A125599 A125600 A125601

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Nov 26 2006

STATUS

approved

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Last modified August 19 18:50 EDT 2019. Contains 326133 sequences. (Running on oeis4.)