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%I M1174 N0451 #27 Jan 22 2018 19:25:49
%S 1,2,4,9,20,45,105,249,599,1463,3614,9016,22695,57564,146985,377555,
%T 974924,2529308,6589734,17234114,45228343,119069228,314368027,
%U 832193902,2208347917,5873364623,15653499416,41800070483,111821751649
%N Number of esters with n carbon atoms.
%D J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008, <a href="/A000632/b000632.txt">Table of n, a(n) for n = 2..99</a>
%H J. L. Faulon, D. Visco and D. Roe, <a href="http://www.cs.sandia.gov/~jfaulon/PUBLICATION/Rev-Comp-Chem.pdf-save">Enumerating Molecules</a>, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%H H. R. Henze and C. M. Blair, <a href="http://dx.doi.org/10.1021/ja01316a050">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
%H H. R. Henze and C. M. Blair, <a href="/A000632/a000632.pdf">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
%H R. C. Read, <a href="/A000598/a000598.pdf">The Enumeration of Acyclic Chemical Compounds</a>, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.
%F G.f.: A(x)=x*B(x)*(B(x)-1), where B(x) = g.f. for A000598. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008
%t terms = 29; (* B = g.f. for A000625 *) B[_] = 0; Do[B[x_] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^(terms+2) // Normal, terms+2];
%t A[x_] = 1*x*B[x]*(B[x] - 1) + O[x]^(terms+2);
%t Drop[CoefficientList[A[x], x], 2] (* _Jean-François Alcover_, Jan 10 2018 *)
%K nonn
%O 2,2
%A _N. J. A. Sloane_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008