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%I #28 Nov 29 2021 10:49:01
%S 0,1,1,1,0,1,-7,1,159,-843,-1231,2359233,-13303471,-271566005,
%T 10142361989,126956968965,-10502027401553,64275615468715,
%U 32481110981976151,-3014479147788009411,-147131182752475409229,14607119841651449406947,1868869263315549659372569
%N Numerators of coefficients in the e.g.f. a(x) such that a(a(x)) = exp(x) - 1.
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.52.
%H Dmitry Kruchinin, Vladimir Kruchinin, <a href="http://arxiv.org/abs/1302.1986">Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$</a>, arXiv:1302.1986 [math.CO], 2013.
%F a(n)/2^A052123(n) = n!*A052104(n)/A052105(n). - _R. J. Mathar_, Sep 25 2011
%e a(x) = x + 1/4*x^2 + 1/48*x^3 + 1/3840*x^5 - 7/92160*x^6 + 1/645120*x^7 + ...
%t 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_ *)
%Y Cf. A052123, A052104, A052105.
%K sign,frac,easy
%O 0,7
%A _N. J. A. Sloane_, Jan 23 2000
%E More terms from _Vladeta Jovovic_, Jul 27 2002
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