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A029868
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Number of connected functions on n points with a loop of length 5.
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3
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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
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OFFSET
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5,3
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LINKS
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FORMULA
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"CIK[ 5 ]" (necklace, indistinct, unlabeled, 5 parts) transform of A000081.
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MATHEMATICA
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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,
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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