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

Absolute values give denominators of constant terms of Fourier series of meromorphic modular forms E_k/Delta, where E_k is the normalized k th Eisenstein series [cf. Gunning or Serre references] and Delta is the normalized unique weight-twelve cusp form for the full modular group (the generating function of Ramanujan's tau function.) - Barry Brent (barrybrent(AT)iphouse.com), Jun 01 2009

|a(n)| is a product of powers of irregular primes (A000928), with the exeception of n = 1,2,3,4,5,7. [From Peter Luschny (peter(AT)luschny.de), Jul 28 2009]

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. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.

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

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

J.-P. Serre, A Course in Arithmetic, Springer-Verlag, 1973, p. 93.

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, 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, 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

For 2 <= k <= 1000 and k != 7, the 2-order of the full constant term of E_k/Delta = 3 + ord_2(k - 7). - Barry Brent (barrybrent(AT)iphouse.com), Jun 01 2009

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.

Cf. A141590

Adjacent sequences: A001064 A001065 A001066 this_sequence A001068 A001069 A001070

Sequence in context: A120084 A141588 A046968 this_sequence A141590 A046988 A029825

sign,frac,nice

N. J. A. Sloane (njas(AT)research.att.com), Richard E. Borcherds (reb(AT)math.berkeley.edu)