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A052122
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Numerators of coefficients in the e.g.f. a(x) such that a(a(x)) = exp(x) - 1.
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5
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0, 1, 1, 1, 0, 1, -7, 1, 159, -843, -1231, 2359233, -13303471, -271566005, 10142361989, 126956968965, -10502027401553, 64275615468715, 32481110981976151, -3014479147788009411, -147131182752475409229, 14607119841651449406947, 1868869263315549659372569
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OFFSET
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0,7
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.52.
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LINKS
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FORMULA
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EXAMPLE
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a(x) = x + 1/4*x^2 + 1/48*x^3 + 1/3840*x^5 - 7/92160*x^6 + 1/645120*x^7 + ...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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