A069076 a(n) = (4*n^2 - 1)^3.

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

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

Cf. A000466, A069075.

Sequence in context: A178631 A226531 A017559 * A128507 A166750 A195374

Adjacent sequences: A069073 A069074 A069075 * A069077 A069078 A069079

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 05 2002

Status

approved