A143280 - OEIS

A143280

Decimal expansion of m(2) = Sum_{n>=0} 1/n!!.

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

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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

G. C. Greubel, Table of n, a(n) for n = 1..10000

Michael Penn, Finding the closed form for a double factorial sum, YouTube video, 2022.

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

Adjacent sequences: A143277 A143278 A143279 * A143281 A143282 A143283

KEYWORD

nonn,cons,changed

AUTHOR

Eric W. Weisstein, Aug 04 2008

STATUS

approved