A335415 Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Formula

Equals 1/2 + Gamma(1/4)^2 / (4*Pi^(3/2)).

Equals 1/2 + sqrt(Pi) / (2*Gamma(3/4)^2).

Example

1.090170299508048113022668970279244293616858317440723649757932199702152...

Maple

evalf(Sum(1/cosh(Pi*k), k=0..infinity), 120);
evalf(1/2 + sqrt(Pi) / (2*GAMMA(3/4)^2), 120);

Mathematica

RealDigits[1/2 + Gamma[1/4]^2/(4*Pi^(3/2)), 10, 120][[1]]

Prog

(PARI) suminf(k=0, 1/cosh(Pi*k))

Crossrefs

Cf. A240964, A254445, A335414. Essentially the same as A249205.

Sequence in context: A197333 A226120 A244593 * A277524 A118811 A200488

Adjacent sequences: A335412 A335413 A335414 * A335416 A335417 A335418

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 08 2020

Status

approved