

A179897


a(n) = (n^(2*n+1) + 1) / (n+1).


3



1, 1, 11, 547, 52429, 8138021, 1865813431, 593445188743, 250199979298361, 135085171767299209, 90909090909090909091, 74619186937936447687211, 73381705110822317661638341, 85180949465178001182799643437, 115244915978498073437814463065839, 179766618030828831251710653305053711
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OFFSET

0,3


COMMENTS

a(n) is the arithmetic mean of the multiset consisting of n lots of 1/n and one lot of n^(2*n+1). This multiset also has an integer valued geometric mean which is equal to n for n > 0.
According to search at OEIS for particular sequence members, a(n) is also: (1+2*n)th qinteger for q=n, (2*(n+1))th cyclotomic polynomial at q=n, Gaussian binomial coefficient [2*n+1, 2*n] for q=n, number of walks of length 1+2*n between any two distinct vertices of the complete graph K_(n+1).


LINKS



FORMULA

a(n) = Sum_{i=0..2*n} (n)^i.


EXAMPLE

For n = 2, a(2) = 11 which is the arithmetic mean of {1/2, 1/2, 2^5} = 33 / 3 = 11. The geometric mean is 8^(1/3) = 2, i.e. both are integral.


PROG

(Python) [(n**(2*n+1)+1)//(n+1) for n in range(1, 11)]
(PARI) a(n) = (n^(2*n + 1) + 1)/(n + 1) \\ Andrew Howroyd, May 03 2023


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

Martin Saturka (martin(AT)saturka.net), Jul 31 2010


EXTENSIONS

Edited, a(0)=1 prepended and more terms from Andrew Howroyd, May 03 2023


STATUS

approved



