A069075 a(n) = (4*n^2 - 1)^2.

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

Offset: 0

Author

Benoit Cloitre, Apr 05 2002

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000466, A123092, A166329.

Programs

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 *)

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