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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)