OFFSET
0,7
REFERENCES
A. Cayley, On the analytical forms called trees, with application to the theory of chemical combinations, Reports British Assoc. Advance. Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 451).
R. C. Read, personal communication.
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
E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees), J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976
MATHEMATICA
n = 50; (* algorithm from Rains and Sloane *)
S2[f_, h_, x_] := f[h, x]^2/2 + f[h, x^2]/2;
S3[f_, h_, x_] := f[h, x]^3/6 + f[h, x] f[h, x^2]/2 + f[h, x^3]/3;
T[-1, z_] := 1; T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S2[T, h-1, z]z, z], n+1];
Sum[Take[CoefficientList[z^(n+1) + S3[T, h-1, z]z - S3[T, h-2, z]z - (T[h-1, z] - T[h-2, z]) (T[h-1, z]-1), z], n+1], {h, 1, n/2}] + PadRight[{1, 1}, n+1] (* Robert A. Russell, Sep 15 2018 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved