

A130834


Decimal expansion of the limit of the (2/n^2)th power of the number of distinct dimer coverings on the n X n square grid, n even, as n goes to infinity.


8



1, 7, 9, 1, 6, 2, 2, 8, 1, 2, 0, 6, 9, 5, 9, 3, 4, 2, 4, 7, 3, 0, 5, 4, 7, 0, 8, 9, 3, 4, 2, 9, 8, 2, 4, 3, 2, 2, 6, 8, 1, 3, 4, 3, 9, 3, 1, 3, 2, 9, 5, 4, 7, 6, 7, 7, 6, 7, 5, 8, 3, 4, 7, 6, 4, 9, 9, 4, 2, 5, 0, 7, 4, 2, 3, 7, 6, 5, 7, 8, 9, 6, 0, 1, 3, 2, 2, 6
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OFFSET

1,2


REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 232.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
S. R. Finch, Several Constants Arising in Statistical Mechanics, Annals Combinat. vol 3 (1999) issue (24) pp. 323335.


FORMULA

Equals exp(2*A006752/A000796).


EXAMPLE

1.791622812069593424730547089...


MAPLE

evalf(exp(2*Catalan/Pi));


MATHEMATICA

RealDigits[Exp[(2*Catalan)/Pi], 10, 120][[1]] (* Harvey P. Dale, Jul 17 2011 *)


PROG

(PARI) exp(2*Catalan/Pi) \\ Charles R Greathouse IV, Jul 15 2014
(MAGMA) R:=RealField(100); Exp(2*Catalan(R)/Pi(R)); // G. C. Greubel, Aug 23 2018


CROSSREFS

Cf. A000796 (Pi), A006752 (Catalan), A229728.
Sequence in context: A222135 A086318 A244674 * A132806 A016629 A154203
Adjacent sequences: A130831 A130832 A130833 * A130835 A130836 A130837


KEYWORD

cons,nonn


AUTHOR

R. J. Mathar, Jul 18 2007


STATUS

approved



