A084248 Decimal expansion of c = Product_{k>=1} (1 + 1/t(k)) where t(k) = k(k+1)/2 is the k-th triangular number.

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

Offset: 1

Author

Benoit Cloitre, Jun 21 2003

Keywords

• cons
• nonn
• changed

Examples

			5.07922020866367833604368795...
		

References

• Bruce C. Berndt, Ramanujan Notebook part II, Infinite series, Springer Verlag, 1989, p. 241.

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000217.

Programs

Mathematica

RealDigits[Cosh[Pi/2*Sqrt[7]]/(2*Pi), 10, 120][[1]] (* Amiram Eldar, Jun 01 2023 *)

PARI

1/2/Pi*cosh(Pi/2*sqrt(7))

Formula

Equals ((1/2)/Pi)*cosh(Pi/2*sqrt(7)).