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

0,2

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