OFFSET
1,1
REFERENCES
Konrad Knopp, Theory and application of infinite series, Dover, p. 269.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
Sum_{n>=1} 1/a(n) = (32 - 3*Pi^3)/64.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(1)=27, a(2)=3375, a(3)=42875, a(4)=250047, a(5)=970299, a(6)=2924207, a(7)=7414875. - Harvey P. Dale, Jan 20 2012
G.f: x*(x^6 - 34*x^5 - 3165*x^4 - 19852*x^3 - 19817*x^2 - 3186*x - 27)/(x-1)^7. - Harvey P. Dale, Jan 20 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^3/128 + 3*Pi/32 - 1/2. - Amiram Eldar, Feb 25 2022
MATHEMATICA
(4Range[30]^2-1)^3 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {27, 3375, 42875, 250047, 970299, 2924207, 7414875}, 30] (* Harvey P. Dale, Jan 20 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved