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 A002861 Number of connected functions (or mapping patterns) on n unlabeled points, or number of rings and branches with n edges. (Formerly M1182 N0455) 16
 1, 2, 4, 9, 20, 51, 125, 329, 862, 2311, 6217, 16949, 46350, 127714, 353272, 981753, 2737539, 7659789, 21492286, 60466130, 170510030, 481867683, 1364424829, 3870373826, 10996890237, 31293083540, 89173833915, 254445242754, 726907585652, 2079012341822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A000081 + A027852 + A029852 + A029853 + A029868 + ... - Geoffrey Critzer, Oct 12 2012 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.6. R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399. 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 Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 500 terms from C. G. Bower) C. G. Bower, Transforms (2) P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 480 R. K. Guy, Letter to N. J. A. Sloane, 1988-04-12 (annotated scanned copy) INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 118 FORMULA CIK transform of A000081. MAPLE spec2861 := [B, {A=Prod(Z, Set(A)), B=Cycle(A)}, unlabeled]; [seq(combstruct[count](spec2861, size=n), n=1..27)]; 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}]; 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, 1, 30}]]  (* Geoffrey Critzer, Oct 12 2012, after code given by Robert A. Russell in A000081 *) 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] ) ); A000081=concat([0], A); H(t)=subst(Ser(A000081, 't), 't, t); x='x+O('x^N); L=sum(j=1, N, eulerphi(j)/j * log(1/(1-H(x^j)))); Vec(L) \\ Joerg Arndt, Jul 10 2014 CROSSREFS Cf. A000081, A001372. Sequence in context: A134955 A171887 A027881 * A032200 A130969 A264293 Adjacent sequences:  A002858 A002859 A002860 * A002862 A002863 A002864 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Philippe Flajolet and Paul Zimmermann, Mar 15 1996 STATUS approved

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Last modified October 20 15:22 EDT 2018. Contains 316388 sequences. (Running on oeis4.)