OFFSET
1,1
COMMENTS
This illustrates the infinite product Pi/2 = Product_{k>=1} ((2*k)/(2k-1))*((2k)/(2k+1)): read the 4 terms of numerator and denominator of the factor in the product in that order shown.
Number of roots of the polynomial 1+x+x^2+...+x^(n+1) = (x^(n+2)-1)/(x-1) in the left half plane. - Michel Lagneau, Oct 30 2012
LINKS
Eric Weisstein's World of Mathematics, Wallis Formula.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-4) - a(n-5).
G.f.: x*(2-x+x^2+x^3-x^4)/((1+x)*(1+x^2)*(1-x)^2).
a(n) = n + 1 - 2*floor( (n+2)/4 ). - M. F. Hasler, Nov 01 2012
a(n) = (2*n + 3 - (-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/4. - Luce ETIENNE, Mar 08 2016
Sum_{n>=1} (-1)^n/a(n) = 2*log(2) - 1. - Amiram Eldar, Sep 10 2023
MATHEMATICA
Flatten[#+{0, -1, 0, 1}&/@Range[2, 40, 2]] (* Harvey P. Dale, Aug 12 2014 *)
PROG
(PARI) A162330(n)=n+1-(n+2)\4*2 \\ M. F. Hasler, Nov 01 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, Jul 01 2009
EXTENSIONS
Edited by R. J. Mathar, Sep 16 2009
STATUS
approved