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A217860 Number of components over all functions on n unlabeled nodes. 0
1, 4, 11, 33, 88, 254, 697, 1984, 5585, 15938, 45424, 130381, 374450, 1079361, 3115291, 9010177, 26090857, 75656608, 219603868, 638075127, 1855506355, 5399995044, 15726096741, 45827313178, 133621409595, 389814176004, 1137757623214, 3322288247568, 9705228070231, 26283373417131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n) = Sum_{k=1..n} A127136(n,k)*k.

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, 1, 30}]], 1]; Drop[CoefficientList[Series[D[Product[1/(1-y x^i)^c[[i]], {i, 1, nn-1}], y]/.y->1, {x, 0, nn}], x], 1]  (* after code given by Robert A. Russell in A000081 *)

CROSSREFS

Sequence in context: A273038 A179905 A034745 * A143787 A289973 A236583

Adjacent sequences:  A217857 A217858 A217859 * A217861 A217862 A217863

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 13 2012

STATUS

approved

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Last modified January 22 09:49 EST 2019. Contains 319363 sequences. (Running on oeis4.)