A060055 Denominators of nonzero numbers appearing in the Euler-Maclaurin summation formula. (See A060054 for the definition of these numbers.)

2, 12, 720, 30240, 1209600, 47900160, 1307674368000, 74724249600, 10670622842880000, 5109094217170944000, 802857662698291200000, 14101100039391805440000, 1693824136731743669452800000

Offset

1,1

Comments

Denominators of nonzero coefficients in the series expansion around zero of cot(x/2)/2, disregarding the first term. - Fredrik Johansson, Aug 20 2006

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

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. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).

Zhanna Kuznetsova, and Francesco Toppan, Classification of minimal Z_2 X Z_2-graded Lie (super)algebras and some applications, arXiv:2103.04385 [math-ph], 2021.

Mathematica

Join[{2}, f[n_]:=Denominator[-(-1)^n BernoulliB[2 n]/(2 n)!]; Table[f[n], {n, 30}]] (* Robert G. Wilson v, Sep 02 2004 *) (* adapted by Vincenzo Librandi, May 04 2017 *)
Join[{2}, Denominator[Table[SeriesCoefficient[x^2/(1 - E^x), {x, 0, n}], {n, 3, 25, 2}]]] (* Terry D. Grant, Jun 01 2017 *)

Prog

(Magma) [2] cat [Denominator(-(-1)^n*Bernoulli(2*n)/Factorial(2*n)): n in [1..15]]; // Vincenzo Librandi, Jun 04 2017

Crossrefs

Numerators give A060054.

Sequence in context: A141770 A363098 A230265 * A363234 A061149 A191555

Adjacent sequences: A060052 A060053 A060054 * A060056 A060057 A060058

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Feb 16 2001

Status

approved