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A029868 Number of connected functions on n points with a loop of length 5. 1
1, 1, 4, 14, 46, 145, 440, 1315, 3877, 11315, 32792, 94529, 271510, 777764, 2223865, 6350657, 18120730, 51680249, 147359335, 420163711, 1198151432, 3417475326, 9750708533, 27831153091, 79471338455, 227032777454, 648896436944, 1855571389651, 5308837191604 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

LINKS

Table of n, a(n) for n=5..33.

C. G. Bower, Transforms

FORMULA

"CIK[ 5 ]" (necklace, indistinct, unlabeled, 5 parts) transform of A000081.

G.f.: A(x) = ( B(x)^5 +4*B(x^5) )/5 where B(x) is the o.g.f. for A000081. - Geoffrey Critzer, Aug 09 2013

MATHEMATICA

nn = 20; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol =

SolveAlways[

  0 == Series[

    f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}],

  x]; b = Flatten[Table[a[n], {n, 1, nn}] /. sol]; CoefficientList[

Series[CycleIndex[CyclicGroup[5], s] /.

   Table[s[i] -> Sum[b[[k]] x^(k*i), {k, 1, nn}], {i, 1, 5}], {x, 0,

nn}], x] (* Geoffrey Critzer, Aug 08 2013 *)

CROSSREFS

Sequence in context: A171851 A117916 A054449 * A030267 A026290 A027649

Adjacent sequences:  A029865 A029866 A029867 * A029869 A029870 A029871

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)