A395411 Decimal expansion of Sum_{k>=2} (zeta(k)-1)*k^2/(k+1).

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

Offset

1,2

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 264, eq. (19).

Links

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

Formula

Equals 3/2 - gamma/2 + zeta(2) - log(2*Pi)/2, where gamma is Euler's constant (A001620).

Example

1.937387701192787264388829385199206333836472759599053...

Mathematica

RealDigits[(3 - EulerGamma - Log[2*Pi])/2 + Zeta[2], 10, 120][[1]]

Prog

(PARI) 3/2 - Euler/2 + zeta(2) - log(2*Pi)/2

Crossrefs

Cf. A001620, A013661, A075700, A396004.

Sequence in context: A068353 A346989 A136251 * A393647 A073002 A357044

Adjacent sequences: A395408 A395409 A395410 * A395412 A395413 A395414

Keyword

nonn,cons

Author

Amiram Eldar, May 22 2026

Status

approved