A145426 Decimal expansion of Sum_{k>=0} (k!/(k+2)!)^2.

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

Offset

0,1

References

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.31.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.19 Vallée's Constant, p. 161.

Links

Table of n, a(n) for n=0..92.

R. J. Mathar, Tightly circumscribed regular polygons, arXiv:1301.6293 [math.MG], 2013, value (A15).

Formula

Equals A002388/3-3 = Sum_{n>=1} 1/A002378(n)^2 = Sum_{n>=2} 1/A035287(n).

Example

0.28986813369645287294483...

Maple

evalf(1/3*Pi^2-3) ;

Mathematica

RealDigits[Pi^2/3 - 3, 10, 120][[1]] (* Amiram Eldar, Jun 17 2023 *)

Prog

(PARI) Pi^2/3-3 \\ Seiichi Manyama, Dec 09 2021
(PARI) sumnumrat(1/(x^4 + 2*x^3 + x^2), 1) \\ Charles R Greathouse IV, Jan 20 2022

Crossrefs

Cf. A002388 (Pi^2), A002378 (oblong numbers), A035287, A348670.

Sequence in context: A081819 A296850 A021349 * A200499 A298525 A350762

Adjacent sequences: A145423 A145424 A145425 * A145427 A145428 A145429

Keyword

cons,easy,nonn

Author

R. J. Mathar, Feb 08 2009

Status

approved