A006956 -id:A006956 - cp's OEIS frontend

A006955 Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

1, 2, 6, 6, 10, 6, 210, 2, 30, 42, 110, 6, 546, 2, 30, 462, 170, 6, 51870, 2, 330, 42, 46, 6, 6630, 22, 30, 798, 290, 6, 930930, 2, 102, 966, 10, 66, 1919190, 2, 30, 42, 76670, 6, 680862, 2, 690, 38874, 470, 6, 46410, 2, 330, 42, 106, 6, 1919190

Offset: 0

Simon Plouffe and N. J. A. Sloane

Also denominators of asymptotic expansion of polygamma function psi''(z).

			(n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260, (6.4.13).
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..1000
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. 260, (6.4.13).
L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.
M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.
Index entries for sequences related to Bernoulli numbers.

Numerators are in A002427.

Cf. A050925/A050932, A000367/A002445, A006956, A123125.

gf := z / (1 - exp(-z)): ser := series(gf, z, 220):
seq(denom((n+1)!*coeff(ser, z, n)), n=0..108, 2); # Peter Luschny, Aug 29 2020

Denominator[Table[(2n+1)BernoulliB[2n],{n,0,60}]] (* Harvey P. Dale, Nov 03 2011 *)

a(n) = denominator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017

Apparently a(n) = denominator(Sum_{k=0..2*n-1} (-1)^(2*n-k+1)*E1(2*n, k+1)/ binomial(2*n, k+1)), where E1(n, k) denotes the first-order Eulerian numbers A123125. - Peter Luschny, Feb 17 2021

A076549 Numerator of (2n+1)(2n+2) B_{2n}, where B_n are the Bernoulli numbers. Also numerators of the asymptotic expansion of the polygamma function psi'''(z).

Original entry on oeis.org

2, 3, 2, -1, 4, -3, 10, -691, 280, -10851, 438670, -1222277, 3418052, -1181820455, 1077690978, -23749461029, 137853460416080, -84802531453387, 541314450257070, -26315271553053477373, 761798417598805340

Offset: 0

Ralf Stephan, Oct 19 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..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].
Abramowitz and Stegun, Handbook of mathematical functions, p. 260 (6.4.14)
Abramowitz and Stegun, Handbook of mathematical functions, p. 260 (6.4.14)

Denominators are in A006956. Cf. A002427/A006955.

Join[{2, 3}, Table[Numerator[(4 n^2 + 6 n + 2) BernoulliB[2 n]], {n, 1, 30}]] (* Vincenzo Librandi, Aug 02 2013 *)

cp's OEIS Frontend

A006955 Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

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