OFFSET
0,2
COMMENTS
Bisection of A027480. For n>1, gives area of triangle two of whose cevians bound three smaller triangles with areas n-1, n, n+1 contiguously. - Lekraj Beedassy, Dec 21 2006
REFERENCES
Eric Harold Neville, Jacobian Elliptic Functions, 2nd ed., 1951, p. 38.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
FORMULA
Sum_{n>=1} 1/a(n) = 2*log(2) - 1. - Benoit Cloitre, Apr 05 2002
a(n) = A204558(2*n) / (2*n). - Reinhard Zumkeller, Jan 18 2012
G.f.: 3*x*(1 + 6*x + x^2)/(1 - x)^4. - Colin Barker, Mar 27 2012
Product_{n>=1} 4*n^3/a(n) = Pi/2. - Daniel Suteu, Feb 05 2017
a(n) = Sum_{i=0..2*n} A046092(n-1)+i = Sum_{i=2*n+1..4*n-1} A046092(n-1)+i for n>0. Example: for n = 5, A046092(4) = 40 and a(5) = 40 + 41 + 42 + ... + 49 + 50 = 51 + 52 + 53 + ... + 58 + 59 = 495. - Bruno Berselli, Oct 26 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - log(2) (A244009). - Amiram Eldar, Jan 30 2021
E.g.f.: exp(x)*x*(3 + 12*x + 4*x^2). - Stefano Spezia, Sep 03 2023
MATHEMATICA
Table[n(2n-1)(2n+1), {n, 0, 40}] (* Harvey P. Dale, Jan 11 2014 *)
PROG
(Magma)[n*(2*n-1)*(2*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 07 2011
(PARI) vector(100, n, (n-1)*(2*n-1)*(2*n-3)) \\ Derek Orr, Jan 29 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Benoit Cloitre, Apr 05 2002
STATUS
approved