OFFSET
0,13
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
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, pp. 998, equ. 27.1.1 for n=1, with a factor (x^2)/2 extracted.
Wolfdieter Lang, Rationals r(n).
FORMULA
a(n) = numerator(r(n)), with r(n) = [x^n]( 1 - 2*x/(2*(2+1)) + Sum_{k >= 0} ((B(2*k)/((k+1)*(2*k)!))*x^(2*k) ), |x|<2*Pi. B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).
a(n) = numerator(2*B(n)/((n+2)*n!)), n >= 0. See the comment on the e.g.f. D(2,x) in A120085. - Wolfdieter Lang, Dec 03 2022
EXAMPLE
Rationals r(n): [1, -1/3, 1/24, 0, -1/2160, 0, 1/120960, 0, -1/6048000, 0, 1/287400960, ...].
MATHEMATICA
max = 38; Numerator[CoefficientList[Integrate[Normal[Series[(2*(t^2/(Exp[t]-1)))/x^2, {t, 0, max}]], {t, 0, x}], x]] (* Jean-François Alcover, Oct 04 2011 *)
Table[Numerator[2*(n+1)*BernoulliB[n]/(n+2)!], {n, 0, 50}] (* G. C. Greubel, May 02 2023 *)
PROG
(Magma) [Numerator(2*(n+1)*Bernoulli(n)/Factorial(n+2)): n in [0..50]]; // G. C. Greubel, May 02 2023
(SageMath) [numerator(2*(n+1)*bernoulli(n)/factorial(n+2)) for n in range(51)] # G. C. Greubel, May 02 2023
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved