A052122 Numerators of coefficients in the e.g.f. a(x) such that a(a(x)) = exp(x) - 1.

0, 1, 1, 1, 0, 1, -7, 1, 159, -843, -1231, 2359233, -13303471, -271566005, 10142361989, 126956968965, -10502027401553, 64275615468715, 32481110981976151, -3014479147788009411, -147131182752475409229, 14607119841651449406947, 1868869263315549659372569

Offset: 0

Author

N. J. A. Sloane, Jan 23 2000

Keywords

• sign
• frac
• easy

Examples

			a(x) = 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.

Links

• Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$, arXiv:1302.1986 [math.CO], 2013.

Crossrefs

Cf. A052123, 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] // Numerator , {n, 0, 22}] (* Jean-François Alcover, Mar 03 2014, after A052104 and Alois P. Heinz *)

Formula

a(n)/2^A052123(n) = n!*A052104(n)/A052105(n). - R. J. Mathar, Sep 25 2011

Extensions

More terms from Vladeta Jovovic, Jul 27 2002