A000632 Number of esters with n carbon atoms up to structural isomerism.

1, 2, 4, 9, 20, 45, 105, 249, 599, 1463, 3614, 9016, 22695, 57564, 146985, 377555, 974924, 2529308, 6589734, 17234114, 45228343, 119069228, 314368027, 832193902, 2208347917, 5873364623, 15653499416, 41800070483, 111821751649

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008, Table of n, a(n) for n = 2..99
• J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
• H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
• H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
• R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.
• Wikipedia, Ester.

Programs

Mathematica

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];
A[x_] = 1*x*B[x]*(B[x] - 1) + O[x]^(terms+2);
Drop[CoefficientList[A[x], x], 2] (* Jean-François Alcover, Jan 10 2018 *)

Formula

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

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008

Name clarified by Sean A. Irvine, Feb 01 2025