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")
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... (A123092) [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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved