login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193548 Decimal expansion of exp(Pi^2/12). 2
2, 2, 7, 6, 1, 0, 8, 1, 5, 1, 6, 2, 5, 7, 3, 4, 0, 9, 4, 7, 9, 1, 0, 6, 1, 4, 1, 2, 0, 3, 1, 4, 9, 7, 4, 4, 6, 6, 9, 7, 9, 7, 4, 2, 6, 0, 3, 0, 0, 2, 3, 7, 7, 5, 6, 1, 5, 5, 1, 6, 1, 7, 0, 9, 8, 2, 7, 5, 0, 6, 3, 7, 2, 8, 6, 3, 0, 1, 4, 3, 1, 8, 6, 6, 8, 4, 6, 5, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..89.

FORMULA

exp(Pi^2/12) = prod(n>=1, prod(k=1..n+1, k^(1/(n+1)) * H(n) * (-1)^k * binom(n, k-1) ) ) where H(n) is the n-th harmonic number.

exp(Pi^2/12) = limit (n -> infinity) Product {k = 1..n} (1 + k/n)^(1/k). - Peter Bala, Feb 14 2015

MATHEMATICA

Product[Product[k^((1/(n+1))*(-1)^(k)*Binomial[n, k-1]*HarmonicNumber[n]), {k, 1, n+1}], {n, 1, Infinity}]

RealDigits[E^(Pi^2/12), 10, 100]

PROG

(PARI) exp(Pi^2/12) \\ Charles R Greathouse IV, Jul 30 2011

CROSSREFS

Cf. A001113, A022493, A122214, A122215, A122216, A122217, A138265, A207651, A242153, A242154, A242155, A242156, A242157, A242158, A242159, A242160, A242161, A242162, A242163, A242164.

Sequence in context: A058625 A300126 A006748 * A131049 A126851 A142070

Adjacent sequences:  A193545 A193546 A193547 * A193549 A193550 A193551

KEYWORD

cons,nonn,easy

AUTHOR

John M. Campbell, Jul 30 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)