OFFSET
1,1
FORMULA
exp(Pi^2/12) = Product_{n>=1} Product_{k=1..n+1} k^(1/(n+1)) * H(n) * (-1)^k * binomial(n, k-1) where H(n) is the n-th harmonic number.
exp(Pi^2/12) = lim_{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
KEYWORD
AUTHOR
John M. Campbell, Jul 30 2011
STATUS
approved