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A069075 a(n) = (4*n^2 - 1)^2. 3
1, 9, 225, 1225, 3969, 9801, 20449, 38025, 65025, 104329, 159201, 233289, 330625, 455625, 613089, 808201, 1046529, 1334025, 1677025, 2082249, 2556801, 3108169, 3744225, 4473225, 5303809, 6245001, 7306209, 8497225, 9828225, 11309769 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Products of squares of 2 successive odd numbers. - Peter Munn, Nov 17 2019
REFERENCES
L. B. W. Jolley, Summation of Series, Dover, 1961.
Konrad Knopp, Theory and application of infinite series, Dover, 1990, 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)) = (Pi^2 - 8)/16 = 0.1168502750680... [Jolley eq. 247]
G.f.: (-1 - 4*x - 190*x^2 - 180*x^3 - 9*x^4) / (x-1)^5. - R. J. Mathar, Oct 03 2011
a(n) = A000466(n)^2. - Peter Munn, Nov 17 2019
E.g.f.: exp(x)*(1 + 8*x + 104*x^2 + 96*x^3 + 16*x^4). - Stefano Spezia, Nov 17 2019
Sum_{n>=0} (-1)^n/a(n) = Pi/8 + 1/2. - Amiram Eldar, Feb 08 2022
MATHEMATICA
(4*Range[0, 30]^2-1)^2 (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 9, 225, 1225, 3969}, 30] (* Harvey P. Dale, Feb 23 2018 *)
CROSSREFS
Sequence in context: A159939 A167038 A074190 * A218659 A012054 A067405
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved

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Last modified April 17 11:14 EDT 2024. Contains 371763 sequences. (Running on oeis4.)