A335538 a(n) = Numerator(-4*n^2*Zeta(1 - n)*Zeta(n)*(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1.

0, 1, 1, 0, -7, 0, 31, 0, -127, 0, 365, 0, -977403607, 0, 57337, 0, -61240067209, 0, 252221719530919, 0, -15984987035583127, 0, 2841046127487821, 0, -468654557583574838590567, 0, 188822581306893585883, 0, -220710643004244238794643249, 0, 1594135539680034434970146279285311

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = numerator(n*Bernoulli(n)*Zeta(n)*(4-2^(3-n))/Pi^n)) for n >= 2.

Example

Rational sequence starts: 0, 1, 1/9, 0, -7/1350, 0, 31/52920, 0, -127/1134000, 0, 365/11290752, ...

Maple

a := s -> `if`(s=1 or s=0, s, -4*s^2*Zeta(1 - s)*Zeta(s)*(1 - 2^(1 - s)) / Pi^s):
seq(numer(a(s)), s = 0..34);

Crossrefs

Cf. A335539 (denominators), A164555/A027642 (Bernoulli numbers).

Cf. A335264, A335265, A327497.

Sequence in context: A279990 A282488 A282492 * A279723 A282268 A279722

Adjacent sequences: A335535 A335536 A335537 * A335539 A335540 A335541

Keyword

sign,frac

Author

Peter Luschny, Jun 13 2020

Status

approved