A335264 -id:A335264 - cp's OEIS frontend

A335265 a(n) = Denominator(-4n^2Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.

1, 1, 3, 1, 15, 1, 7, 1, 15, 1, 33, 1, 455, 1, 3, 1, 255, 1, 133, 1, 33, 1, 69, 1, 455, 1, 3, 1, 435, 1, 2387, 1, 255, 1, 3, 1, 319865, 1, 3, 1, 1353, 1, 43, 1, 345, 1, 141, 1, 7735

Offset: 0

Peter Luschny, Jun 13 2020

			Rational sequence starts: 0, 1, 1/3, 0, 1/15, 0, 1/7, 0, 17/15, 0, 775/33, 0, 477481/455, ...

Cf. A335264 (numerators), A164555/A027642 (Bernoulli numbers).

Cf. A335538, A335539, A327497.

a := s -> `if`(s = 0, 0, -4*s^2*Zeta(1 - s)^2*(1 - 2^s)):
seq(denom(a(s)), s = 0..24);

a(n) = denominator(Bernoulli(n)^2*(2^(n+2) - 4)).

A335538 a(n) = numerator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1.

Original entry on oeis.org

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

Peter Luschny, Jun 13 2020

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

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

Cf. A335264, A335265, A327497.

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);

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

A335539 a(n) = denominator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 1, a(1) = 1.

Original entry on oeis.org

1, 1, 9, 1, 1350, 1, 52920, 1, 1134000, 1, 11290752, 1, 74373979680000, 1, 8006169600, 1, 12147360825600000, 1, 56625794240311296000, 1, 3311787858630451200000, 1, 451287524451778560000, 1, 48168123888308960600064000000, 1, 10738530029998374912000000, 1

Offset: 0

Peter Luschny, Jun 13 2020

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

Cf. A335538 (numerators), A164555/A027642 (Bernoulli numbers).

Cf. A335264, A335265, A327497.

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

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

cp's OEIS Frontend

A335265 a(n) = Denominator(-4n^2Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.

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A335538 a(n) = numerator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1.

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Examples

Crossrefs

Programs

Maple

Formula

A335539 a(n) = denominator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 1, a(1) = 1.

Views

Author

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Examples

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Maple

Formula

cp's OEIS Frontend

A335265 a(n) = Denominator(-4*n^2*Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Formula

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Formula

A335539 a(n) = denominator(-4*n^2*zeta(1 - n)*zeta(n)*(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 1, a(1) = 1.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Formula

A335265 a(n) = Denominator(-4n^2Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.

A335538 a(n) = numerator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1.

A335539 a(n) = denominator(-4n^2zeta(1 - n)zeta(n)(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 1, a(1) = 1.