A227830 Denominators of coefficients in expansion of x/(exp(x)-1).

1, 2, 12, 1, 720, 1, 30240, 1, 1209600, 1, 47900160, 1, 1307674368000, 1, 74724249600, 1, 10670622842880000, 1, 5109094217170944000, 1, 802857662698291200000, 1, 14101100039391805440000, 1, 1693824136731743669452800000, 1, 186134520519971831808000000, 1, 37893265687455865519472640000000, 1, 759790291646040068357842010112000000, 1

Offset: 0

Author

N. J. A. Sloane, Aug 01 2013

Keywords

• nonn
• frac

Examples

			1, -1/2, 1/12, 0, -1/720, 0, 1/30240, 0, -1/1209600, 0, 1/47900160, 0, -691/1307674368000, 0, 1/74724249600, 0, ...
		

References

• M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 23.

Crossrefs

For numerators see A120082.

Cf. A060054, A060055.

Programs

Mathematica

Denominator[ CoefficientList[ Series[x/(1 - E^-x), {x, 0, 26}], x]] (* Robert G. Wilson v, Dec 29 2016 *)

Sage

@cached_function
def R(n): return -sum(R(k)/factorial(n-k+1) for k in (0..n-1)) if n>0 else 1
print([R(n).denominator() for n in (0..31)]) # Peter Luschny, Jul 30 2015

Formula

Recurrence: R(0) = 1 and R(n) = - Sum_{k=0..n-1} R(k)/(n-k+1)! for n>=1. Then a(n) = denominator(R(n)). - Peter Luschny, Jul 30 2015