OFFSET
0,4
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 70, Table 3.4.1.
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
Joerg Arndt, Table of n, a(n) for n = 0..508
Frank Harary, The number of functional digraphs, Mathematische Annalen, 138.3 (1959): 203-210. - From N. J. A. Sloane, Apr 08 2014
Ronald C. Read, Note on number of functional digraphs, Math. Ann., vol. 143 (1961), pp. 109-111.
N. J. A. Sloane, Transforms
L. Travis, Graphical Enumeration: A Species-Theoretic Approach, arXiv:math/9811127 [math.CO], 1998.
James Turner and William H. Kautz, A survey of progress in graph theory in the Soviet Union, SIAM Rev. 12 1970 suppl. iv+68 pp. MR0268074 (42 #2973). See p. 20 concerning calculation of a(n) for n <= 25 by Zakrevskii in 1961. - N. J. A. Sloane, Apr 08 2014
FORMULA
Euler transform of A002862.
G.f.: (x/T(x)) / Product_{n>=1} ( 1 - T(x^n) ) where T(x) is the g.f. of A000081, see the Read reference and the PARI code. - Joerg Arndt, Apr 17 2014
MATHEMATICA
Needs["Combinatorica`];
nn=30; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2 k, 0, s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i] s[n-1, i] i, {i, 1, n-1}]/(n-1); rt=Table[a[i], {i, 1, nn}]; c=Drop[Apply[Plus, Table[Take[CoefficientList[CycleIndex[CyclicGroup[n], s]/.Table[s[j]->Table[Sum[rt[[i]] x^(k*i), {i, 1, nn}], {k, 1, nn}][[j]], {j, 1, nn}], x], nn], {n, 2, 30}]], 1]; CoefficientList[Series[Product[1/(1-x^i)^c[[i]], {i, 1, nn-1}], {x, 0, nn}], x] (* after code given by Robert A. Russell in A000081 *) (* Geoffrey Critzer, Oct 12 2012 *)
PROG
(PARI)
N=66; A=vector(N+1, j, 1);
for (n=1, N, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) );
v0000081=concat([0], A); \\ A000081
x='x+O('x^N); T = Ser(v0000081);
gf = x/T / prod(n=1, N, 1 - subst(T, 'x, 'x^n) );
v001373 = Vec(gf) \\ Joerg Arndt, Apr 17 2014
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Sequence extended by Paul Zimmermann
More terms and better description from Christian G. Bower
More terms added by Joerg Arndt, Apr 17 2014
STATUS
approved