A145429 Decimal expansion of Sum_{n > 0} n*(n!)^2/(2n)!.

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

Offset

1,3

Comments

Also, decimal expansion of Sum_{n >= 0} n/binomial(2*n, n). - Bruno Berselli, Sep 14 2015

References

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.35.

Links

Table of n, a(n) for n=1..93.

Formula

Equals 10*A021139*(9+A000796*A002194).

From Amiram Eldar, Nov 16 2021: (Start)

Equals 2/3 + 2*Pi/(9*sqrt(3)).

Equals 1 + Integral_{x>=1} 1/(x^2 + x + 1)^2 dx. (End)

Example

1.069733192052..

Maple

2/3+2/27*Pi*3^(1/2) ;

Mathematica

RealDigits[2/3 + 2*Pi/(9*Sqrt[3]), 10, 100][[1]] (* Amiram Eldar, Nov 16 2021 *)

Crossrefs

Cf. A010722 (decimal expansion of Sum_{n >= 0} n/binomial(2*n+1, n)).

Cf. A000796, A002194, A021139.

Sequence in context: A283743 A339764 A229921 * A194789 A273082 A065414

Adjacent sequences: A145426 A145427 A145428 * A145430 A145431 A145432

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 08 2009

Status

approved