A127198 Value of the Foxtrot sum Sum_{k>=1} (-1)^(k + 1)*k^2/(k^3 + 1).

2, 3, 9, 5, 6, 0, 7, 4, 7, 3, 4, 0, 7, 4, 1, 9, 4, 9, 8, 7, 8, 1, 5, 3, 2, 5, 1, 1, 3, 8, 0, 3, 4, 1, 5, 1, 4, 8, 0, 1, 0, 8, 6, 2, 3, 9, 9, 3, 3, 6, 9, 4, 0, 8, 6, 0, 1, 1, 9, 6, 3, 5, 9, 3, 9, 6, 7, 3, 1, 4, 1, 5, 5, 3, 8, 2, 3, 1, 2, 8, 1, 6, 9, 8, 2, 6, 4, 6, 8, 4, 6, 1, 0, 6, 3, 2, 2, 7, 3, 5, 6, 6, 5, 8, 1

Offset

0,1

Comments

The calculation of this sum is one of the four questions in the exam given to Paige Fox in the June 2, 1996 comic strip FoxTrot by Bill Amend. - Amiram Eldar, Jun 27 2021

References

Bill Amend, Camp Foxtrot, Kansas City, MO: Andrews McMeel Publishing, 1998, p. 19.

Bill Amend, The Best of FoxTrot, Kansas City, MO: Andrews McMeel Publishing, 2010, p. 212.

Links

Table of n, a(n) for n=0..104.

Richard Askey, The "Foxtrot" sum: Homage to Euler on the 300th anniversary of his birth, The Mathematics Teacher, Vol. 101, No. 6 (2008), pp. 404-406.

Margaret Cibes and James Greenwood, Media Clips, The Mathematics Teacher, Vol. 100, No. 5 (2006/2007), pp. 338-342.

Eric Weisstein's World of Mathematics, Foxtrot Series.

Formula

Equals (1 - log(2) + Pi*sech((sqrt(3)*Pi)/2))/3.

Example

0.23956074734074194987815325113803415148010862399336...

Mathematica

RealDigits[(1 - Log[2] + Pi*Sech[(Sqrt[3]*Pi)/2])/3, 10, 100][[1]]

Prog

(PARI) sumalt(k=1, (-1)^(k + 1)*k^2/(k^3 + 1)) \\ Michel Marcus, Jun 27 2021

Crossrefs

Sequence in context: A229212 A210586 A202017 * A065631 A222244 A325645

Adjacent sequences: A127195 A127196 A127197 * A127199 A127200 A127201

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 08 2007

Status

approved