cp's OEIS Frontend

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

%I A000632 M1174 N0451 #40 Feb 05 2025 10:12:54
%S A000632 1,2,4,9,20,45,105,249,599,1463,3614,9016,22695,57564,146985,377555,
%T A000632 974924,2529308,6589734,17234114,45228343,119069228,314368027,
%U A000632 832193902,2208347917,5873364623,15653499416,41800070483,111821751649
%N A000632 Number of esters with n carbon atoms up to structural isomerism.
%D A000632 J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%D A000632 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000632 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000632 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 A000632 J. L. Faulon, D. Visco and D. Roe, <a href="https://doi.org/10.1002/0471720895.ch3">Enumerating Molecules</a>, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%H A000632 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 A000632 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 A000632 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.
%H A000632 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ester">Ester</a>.
%F A000632 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 A000632 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 A000632 A[x_] = 1*x*B[x]*(B[x] - 1) + O[x]^(terms+2);
%t A000632 Drop[CoefficientList[A[x], x], 2] (* _Jean-François Alcover_, Jan 10 2018 *)
%K A000632 nonn
%O A000632 2,2
%A A000632 _N. J. A. Sloane_
%E A000632 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008
%E A000632 Name clarified by _Sean A. Irvine_, Feb 01 2025