Template:Sequence of the Day for November 27

Intended for: November 27, 2012

Timetable

• First draft entered by Alonso del Arte on April 1, 2012 (based on remarks from Robert Israel et al) ✓
• Draft to be reviewed by September 27, 2012
• Draft to be approved by October 27, 2012

Yesterday's SOTD * Tomorrow's SOTD

A164003: Decimal expansion of

e  − π 2 / 2

.

0.00719188335582...

One has to be careful about branches of multivalued complex functions. By definition

(e i ) π  i

is

e  π  i  log (e i )

(using any of the branches of the logarithm function)

= e  π  i  (1 + π  i  / 2 + 2 n π  i )

(for any integer

n

)

=  −  (e  −  π 2 / 2   −   2 n  π 2 )

. There is no imaginary part in any of its branches. If

n = 0

we get

( − 1)

times the present constant.

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Thanksgiving 2014 falls on November 27.

The line below marks the end of the <noinclude> ... </noinclude> section.

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A000055: Number of trees with

n, n   ≥   0,

unlabeled nodes.

{ 1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235, ... }

Trees with

n

unlabeled nodes

n	Trees
0	Null tree
1	●
2	●—●
3	●—●—●
4	● / ●—●—●—● ●—● \ ●
5	● ● / | ●—●—●—●—● ●—●—● ●—●—● \ | ● ●

This is the sequence for the example search on the front page of the OEIS. This Thanksgiving we are thankful for, among other things, the OEIS, which is an invaluable resource in many mathematical and scientific endeavors.

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