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A143280 Decimal expansion of m(2) = Sum_{n>=0} 1/n!!. 17
3, 0, 5, 9, 4, 0, 7, 4, 0, 5, 3, 4, 2, 5, 7, 6, 1, 4, 4, 5, 3, 9, 4, 7, 5, 4, 9, 9, 2, 3, 3, 2, 7, 8, 6, 1, 2, 9, 7, 7, 2, 5, 4, 7, 2, 6, 3, 3, 5, 3, 4, 0, 2, 0, 9, 2, 9, 9, 7, 1, 8, 7, 7, 9, 8, 0, 5, 4, 4, 2, 8, 1, 9, 6, 8, 4, 6, 1, 3, 5, 3, 5, 7, 4, 8, 1, 8, 5, 7, 4, 4, 8, 3, 4, 9, 7, 8, 2, 8, 3, 1, 5, 0, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also decimal expansion of Sum_{n>=1} n!!/n!. - Michel Lagneau, Dec 24 2011
Apart from the first digit, the same as A227569. - Robert G. Wilson v, Apr 09 2014
LINKS
Eric Weisstein's World of Mathematics, Double Factorial
Eric Weisstein's World of Mathematics, Reciprocal Multifactorial Constant
FORMULA
Equals sqrt(e) + sqrt((e*Pi)/2)*erf(1/sqrt(2)).
EXAMPLE
3.05940740534257614453947549923327861297725472633534020929971877980544281968...
MATHEMATICA
RealDigits[ Sqrt[E] + Sqrt[E*Pi/2]*Erf[1/Sqrt[2]], 10, 105][[1]] (* or *)
RealDigits[ Sum[1/n!!, {n, 0, 125}], 10, 105][[1]] (* Robert G. Wilson v, Apr 09 2014 *)
RealDigits[Total[1/Range[0, 200]!!], 10, 120][[1]] (* Harvey P. Dale, Apr 10 2022 *)
PROG
(PARI) default(realprecision, 100); exp(1/2)*(1 + sqrt(Pi/2)*(1-erfc(1/sqrt(2) ))) \\ G. C. Greubel, Mar 27 2019
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1/2)*(1 + Sqrt(Pi(R)/2)*Erf(1/Sqrt(2) )) // G. C. Greubel, Mar 27 2019
(Sage) numerical_approx(exp(1/2)*(1 + sqrt(pi/2)*erf(1/sqrt(2))), digits=100) # G. C. Greubel, Mar 27 2019
CROSSREFS
Cf. A227569.
Cf. A006882 (n!!), this sequence (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), A288093 (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).
Sequence in context: A181835 A076296 A260934 * A326988 A088521 A022837
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 04 2008
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)