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%I #11 Jul 03 2018 02:33:28
%S 1,1,4,9,28,71,198,521,1418,3773,10153,27114,72705,194531,521447,
%T 1397482,3749836,10067417,27057233,72779710,195963184,528127752,
%U 1424707167,3846943003,10397057771,28125235102,76149287981,206351312858,559642013499,1519019192097
%N Number of monocyclic skeletons with n carbon atoms and a ring size of 5.
%D Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
%H Andrew Howroyd, <a href="/A120333/b120333.txt">Table of n, a(n) for n = 5..200</a>
%e If n=10 then the number of monocyclic skeletons with ring size of five is 71.
%t G[n_] := Module[{g}, Do[g[x_] = 1 + x*(g[x]^3/6 + g[x^2]*g[x]/2 + g[x^3]/3) + O[x]^n // Normal, {n}]; g[x]];
%t T[n_, k_] := Module[{t = G[n], g}, t = x*((t^2 + (t /. x -> x^2))/2); g[e_] = (Normal[t + O[x]^Quotient[n, e]] /. x -> x^e) + O[x]^n // Normal; Coefficient[(Sum[EulerPhi[d]*g[d]^(k/d), {d, Divisors[k]}]/k + If[OddQ[ k], g[1]*g[2]^Quotient[k, 2], (g[1]^2 + g[2])*g[2]^(k/2-1)/2])/2, x, n]];
%t a[n_] := T[n + 5, 5];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jul 03 2018, after _Andrew Howroyd_ *)
%Y Column k=5 of A305059.
%K nonn
%O 5,3
%A _Parthasarathy Nambi_, Aug 13 2006
%E More terms from _N. J. A. Sloane_, Aug 27 2006
%E Terms a(26) and beyond from _Andrew Howroyd_, May 24 2018
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