A193548 Decimal expansion of exp(Pi^2/12).

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

Links

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

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

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 A142070 A152825

Adjacent sequences: A193545 A193546 A193547 * A193549 A193550 A193551

Keyword

cons,nonn,easy

Author

John M. Campbell, Jul 30 2011

Status

approved