A247398 Decimal expansion of a constant 'v' such that the asymptotic variance of the distribution of the longest cycle given a random n-permutation evaluates as v*n^2.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

Links

Table of n, a(n) for n=0..96.

Eric Weisstein's MathWorld, Golomb-Dickman Constant

Wikipedia, Golomb-Dickman constant

Formula

v = integral_{0..infinity} x-e^Ei(-x)*x dx - (integral_{0..infinity} 1-e^Ei(-x) dx)^2, where Ei is the exponential integral function. [corrected by Vaclav Kotesovec, Aug 12 2019]

Example

0.03690783006485220217710700292932764...

Maple

evalf(int((x-exp(Ei(-x))*x), x=0..infinity) - int( (1-exp(Ei(-x))), x=0..infinity)^2, 50); # Vaclav Kotesovec, Aug 12 2019

Mathematica

v = NIntegrate[x - E^ExpIntegralEi[-x]*x, {x, 0, Infinity}, WorkingPrecision -> 80] - NIntegrate[1 - E^ExpIntegralEi[-x], {x, 0, Infinity}, WorkingPrecision -> 80]^2; Join[{0}, RealDigits[v, 10, 40] // First]

Crossrefs

Cf. A084945.

Sequence in context: A197292 A232817 A346640 * A094560 A179615 A183033

Adjacent sequences: A247395 A247396 A247397 * A247399 A247400 A247401

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 16 2014

Extensions

More digits from Vaclav Kotesovec, Aug 12 2019

Status

approved