The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A179897 Numbers a_n with property that a(n) is arithmetic mean of sequence "n-times n^-1, once n^(2*n+1)" that has integer valued both arithmetic and geometric means even though some of the sequence members are (for n>1) non-integer. 0
 1, 11, 547, 52429, 8138021, 1865813431, 593445188743, 250199979298361, 135085171767299209, 90909090909090909091 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS According to search at OEIS for particular sequence members, a(n) is also: (1+2*n)-th q-integer 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) = (n^(2*n+1) + 1) / (n+1). a(n) = \sum_{i=0}^{2*n} (-n)^i. EXAMPLE For n = 2 the a(2) = 11 since arithmetic mean of (1/2, 1/2, 2^5) is 33 / 3 = 11 where its 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)] CROSSREFS Values for n = 5, 6 via other ways. Q-integers: A014986, A014987, K_n paths: A015531, A015540, Cyclotomic polynomials: A020504, A020505, Gaussian binomial coefficients: A015391, A015429. Sequence in context: A065823 A233198 A049654 * A185203 A265978 A263184 Adjacent sequences:  A179894 A179895 A179896 * A179898 A179899 A179900 KEYWORD easy,nonn AUTHOR Martin Saturka (martin(AT)saturka.net), Jul 31 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)