A000632 Number of esters with n carbon atoms. (Formerly M1174 N0451)

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

2,2

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.

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

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 *)

Crossrefs

Sequence in context: A352018 A188460 A111099 * A090245 A274965 A006958

Adjacent sequences: A000629 A000630 A000631 * A000633 A000634 A000635

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved