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

Author

N. J. A. Sloane, Jan 23 2000

Keywords

• nonn
• frac
• easy

Examples

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

References

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

Crossrefs

Cf. A052122, A052104, A052105.

Programs

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 *)

Extensions

More terms from Vladeta Jovovic, Jul 27 2002

More terms from Sean A. Irvine, Oct 25 2021