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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
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
KEYWORD
cons,nonn,easy
AUTHOR
John M. Campbell, Jul 30 2011
STATUS
approved