A393668 Decimal expansion of log(sinh(Pi)/Pi).

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

Offset

1,2

Comments

Arrives as the k=2 case of the arctanh power sums 2*h(k) = Sum_{n>=2} arctanh(1/n^k).

Links

Table of n, a(n) for n=1..106.

Ryan Goulden, Closed-Form Evaluation of arctanh Power Sums via Infinite Products, arXiv:2602.06244 [math.GM], 2026.

Formula

Equals log(sinh(Pi)/Pi) = log(A156648).

Equals 2 * Sum_{n>=2} arctanh(1/n^2).

Equals 2*Sum_{k>=0} (zeta(2*(2*k+1)) - 1) / (2*k+1).

Equals -2*A352527. - Hugo Pfoertner, Feb 24 2026

Example

1.301846398603712677770433663...

Mathematica

RealDigits[Log[Sinh[Pi]/Pi], 10, 106][[1]]

Prog

(PARI) log(sinh(Pi)/Pi)

Crossrefs

Cf. A000796, A090986, A156648, A352527.

Sequence in context: A291763 A161129 A011074 * A020816 A385910 A378062

Adjacent sequences: A393665 A393666 A393667 * A393669 A393670 A393671

Keyword

nonn,cons

Author

Ryan Goulden, Feb 24 2026

Status

approved