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

Author

R. J. Mathar, Feb 08 2009

Keywords

• cons
• easy
• nonn

Examples

			0.28986813369645287294483...
		

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

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

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

Formula

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