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

Offset: 1

Author

Eric W. Weisstein, Aug 04 2008

Keywords

• nonn
• cons

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

Examples

			3.05940740534257614453947549923327861297725472633534020929971877980544281968...
		

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

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)).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1/2)*(1 + Sqrt(Pi(R)/2)*Erf(1/Sqrt(2) )); // G. C. Greubel, Mar 27 2019

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 *)

PARI

default(realprecision, 100); exp(1/2)*(1 + sqrt(Pi/2)*(1-erfc(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

Formula

Equals sqrt(e) + sqrt((e*Pi)/2)*erf(1/sqrt(2)).