A052123 Log_2 of denominators of coefficients in the e.g.f. a(x) such that a(a(x)) = exp(x) - 1.

0, 0, 1, 3, 0, 5, 7, 7, 8, 8, 12, 14, 14, 15, 16, 18, 18, 19, 21, 24, 24, 26, 28, 29, 26, 27, 32, 34, 35, 35, 37, 36, 38, 39, 40, 41, 43, 46, 48, 49, 47, 50, 53, 55, 55, 56, 58, 59, 57, 56, 61, 64, 64, 66, 68, 70, 70, 71, 73, 75, 76, 76, 76, 78, 78, 79, 80, 82

Offset

0,4

References

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.52.

Links

Table of n, a(n) for n=0..67.

Example

x + (1/4)*x^2 + (1/48)*x^3 + (1/3840)*x^5 - (7/92160)*x^6 + (1/645120)*x^7 + ...

Mathematica

T[n_, n_] = 1; T[n_, m_] := T[n, m] = (StirlingS2[n, m]*m!/n! - Sum[T[n, i]*T[i, m], {i, m+1, n-1}])/2; Table[n!*T[n, 1] // Denominator // Log[2, #]&, {n, 0, 29}] (* Jean-François Alcover, Mar 03 2014, after A052104 and Alois P. Heinz *)

Crossrefs

Cf. A052122, A052104, A052105.

Sequence in context: A350082 A362241 A019915 * A285471 A258113 A174190

Adjacent sequences: A052120 A052121 A052122 * A052124 A052125 A052126

Keyword

nonn,frac,easy

Author

N. J. A. Sloane, Jan 23 2000

Extensions

More terms from Vladeta Jovovic, Jul 27 2002

More terms from Sean A. Irvine, Oct 25 2021

Status

approved