A069073 a(n) = n*(4n^2 - 1)^2.

0, 9, 450, 3675, 15876, 49005, 122694, 266175, 520200, 938961, 1592010, 2566179, 3967500, 5923125, 8583246, 12123015, 16744464, 22678425, 30186450, 39562731, 51136020, 65271549, 82372950, 102884175, 127291416, 156125025, 189961434, 229425075, 275190300, 327983301

Offset: 0

Author

Benoit Cloitre, Apr 05 2002

Keywords

• easy
• nonn

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, eq. (104) on page 20.
• Konrad Knopp, Theory and application of infinite series, Dover, 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")

Crossrefs

Cf. A006752, A069075.

Programs

Mathematica

a[n_] := n*(4*n^2 - 1)^2; Array[a, 40, 0] (* Amiram Eldar, Mar 08 2022 *)

Formula

Sum_{n>=1} 1/a(n) = 3/2 -2*log(2) = 0.113705638880109...

Sum_{n>=1} (-1)^(n+1)/a(n) = G + log(2) - 3/2, where G is Catalan's constant (A006752). - Amiram Eldar, Mar 08 2022