login
A069076
a(n) = (4*n^2 - 1)^3.
1
27, 3375, 42875, 250047, 970299, 2924207, 7414875, 16581375, 33698267, 63521199, 112678587, 190109375, 307546875, 480048687, 726572699, 1070599167, 1540798875, 2171747375, 3004685307, 4088324799, 5479701947, 7245075375
OFFSET
1,1
REFERENCES
Konrad Knopp, Theory and application of infinite series, Dover, p. 269.
LINKS
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) = (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
Sequence in context: A178631 A226531 A017559 * A128507 A166750 A195374
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved