1,6

Also numerator of "modified Bernoulli number" b(2n) = Bernoulli(2*n)/(2*n*n!). Denominators are in A057868.

Ramanujan incorrectly conjectured that the sequence contains only primes (and 1) [ Jud McCranie (j.mccranie(AT)comcast.net) ]. See A112548, A119766.

a(n)=A046968(n) if n<574; a(574)=37*A046968(574). - Michael Somos Feb 01 2004

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 259, (6.3.18) and (6.3.19); also p. 810.

L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205

R. Kanigel, The Man Who Knew Infinity, pp. 91-92.

J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton, 1974, p. 285.

T. D. Noe, Table of n, a(n) for n=1..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 1972, p. 259, (6.3.18) and (6.3.19).

D. Bar-Natan, T. T. Q. Le and D. P. Thurston, Two applications of elmentary knot theory ... Geometry and Topology 7-1 (2003) 1-31.

G. Everest, A. J. van der Poorten, Y. Puri and T. Ward, Integer Sequences and Periodic Points, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.3

E. Z. Goren, Table of values of Riemann zeta function

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (3).

Eric Weisstein's World of Mathematics, Modified Bernoulli Numbers.

Index entries for sequences related to Bernoulli numbers.

Zeta(1-2n) = - Bernoulli(2n)/(2n).

G.f.: numerators of coefficients of z^2n in z/(exp(z)-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 02 2003

The sequence Bernoulli(2n)/(2n) (n >= 1) begins 1/12, -1/120, 1/252, -1/240, 1/132, -691/32760, 1/12, -3617/8160, ...

The sequence of modified Bernoulli numbers begins 1/48, -1/5760, 1/362880, -1/19353600, 1/958003200, -691/31384184832000, ...

Table[ Numerator[ BernoulliB[2n]/(2n)], {n, 1, 22}] (from Robert G. Wilson v Feb 03 2004)

(PARI) a(n)=if(n<1, 0, numerator(bernfrac(2*n)/(2*n)))

Similar to but different from A046968. See A090495, A090496.

Denominators given by A006953. Cf. A000367, A033563, A006863, A046968.

Sequence in context: A120082 A120084 A046968 this_sequence A046988 A029825 A106281

Adjacent sequences: A001064 A001065 A001066 this_sequence A001068 A001069 A001070

sign,frac,nice

njas, Richard E. Borcherds (reb(AT)math.berkeley.edu)