A029868 Number of connected functions on n points with a loop of length 5.

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

Offset

5,3

Links

Andrew Howroyd, Table of n, a(n) for n = 5..500

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

a(n) ~ A187770 * A051491^n / n^(3/2). - Vaclav Kotesovec, Dec 25 2020

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

Column 5 of A339428.

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