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 A001373 Functional digraphs (digraphs of functions on n nodes where every node has outdegree 1 and loops of length 1 are forbidden). (Formerly M1597 N0623) 11
 1, 0, 1, 2, 6, 13, 40, 100, 291, 797, 2273, 6389, 18264, 51916, 148666, 425529, 1221900, 3511507, 10111043, 29142941, 84112009, 243000149, 702758065, 2034150215, 5892907566, 17084615940, 49567063847, 143902155133, 418032946298, 1215076634226, 3533715961160, 10282042126394, 29931877173282, 87173224346464, 253989569994664 (list; graph; refs; listen; history; text; internal format)
 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. Turner, James; Kautz, William H., 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 Cf. A001372. Sequence in context: A124124 A052450 A231385 * A284223 A241784 A211995 Adjacent sequences:  A001370 A001371 A001372 * A001374 A001375 A001376 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

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