%I M1588 N0618 #27 Dec 19 2021 09:41:49
%S 1,2,6,12,31,72,178,430,1071,2654,6680,16858,42926,109778,282490,
%T 730028,1895456,4940094,12923600,33919416,89301052,235762572,
%U 624057892,1655817422,4403189781,11733247076,31326037116,83786187152,224475807465
%N Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms.
%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 T. D. Noe, <a href="/A000650/b000650.txt">Table of n, a(n) for n=0..200</a>
%H G. Polya, <a href="http://dx.doi.org/10.1524/zkri.1936.93.1.415">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>, Zeit. f. Kristall., 93 (1936), 415-443; last line of Table I.
%H G. Polya, <a href="/A000598/a000598_3.pdf">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>, Zeit. f. Kristall., 93 (1936), 415-443; Table I, last line. (Annotated scanned copy)
%F G.f.: A(x) = (r(x)^4+r(x^2)^2)/2, r(x) = A000598(x).
%t terms = 29; (* r = g.f. of A000598 *) r[_] = 0; Do[r[x_] = 1 + (1/6)*x*(r[x]^3 + 3*r[x]*r[x^2] + 2*r[x^3]) + O[x]^terms // Normal, terms];
%t A[x_] = (r[x]^4 + r[x^2]^2)/2 + O[x]^terms;
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Jan 25 2012, updated Jan 10 2018 *)
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_