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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 Table of n, a(n) for n=0..29. 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 (5,-10,10,-5,1). 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 Cf. A000466, A166329. Sequence in context: A159939 A167038 A074190 * A218659 A012054 A067405 Adjacent sequences: A069072 A069073 A069074 * A069076 A069077 A069078 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.)