A232248
Denominators of the expected length of a random cycle in a random permutation.
Original entry on oeis.org
1, 2, 12, 24, 720, 1440, 60480, 4480, 3628800, 1036800, 479001600, 958003200, 2615348736000, 172204032, 2414168064000, 62768369664000, 2462451425280000, 9146248151040000, 51090942171709440000, 136216903680000, 33720021833328230400000, 67440043666656460800000
Offset: 1
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with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
expand(add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j
*b(n-i*j, i-1) *x^j, j=0..n/i))))
end:
a:= n->denom((p->add(coeff(p, x, i)/i, i=1..n))(b(n$2))/(n-1)!):
seq(a(n), n=1..30); # Alois P. Heinz, Nov 21 2013
# second Maple program:
a:= n-> denom(add(abs(combinat[stirling1](n, i))/i, i=1..n)/(n-1)!):
seq(a(n), n=1..30); # Alois P. Heinz, Nov 23 2013
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Table[Denominator[Total[Map[Total[#]!/Product[#[[i]],{i,1,Length[#]}]/Apply[Times,Table[Count[#,k]!,{k,1,Max[#]}]]/(Total[#]-1)!/Length[#]&,Partitions[n]]]],{n,1,25}]
A266581
Numerators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.
Original entry on oeis.org
1, 15, 1145, 7795, 10605889, 59526571, 139954552433, 34217723087, 806539298609929, 3932874930141827, 4100492004734957581, 96658551584623754987, 838219558485468722155050481, 142916593419748754034403361, 158366688967470905539833679601, 102317913027622943383626250477
Offset: 0
1, 15/4, 1145/144, 7795/576, 10605889/518400, 59526571/2073600, 139954552433/3657830400, 34217723087/696729600, 806539298609929/13168189440000, …
Cf.
A232193 (numerators of expansion of PolyLog(-1, x)/PolyLog(1, x)),
A232248 (denominators of expansion of PolyLog(-1, x)/PolyLog(1, x)).
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Table[Numerator[SeriesCoefficient[PolyLog[-2, x]/PolyLog[2, x], {x, 0, n}]], {n, 0, 15}]
A273698
Denominators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.
Original entry on oeis.org
1, 4, 144, 576, 518400, 2073600, 3657830400, 696729600, 13168189440000, 52672757760000, 45888506560512000, 917770131210240000, 6840049010896797696000000, 1013340594206932992000000, 984967057569138868224000000, 562838318610936496128000000
Offset: 0
1, 15/4, 1145/144, 7795/576, 10605889/518400, 59526571/2073600, 139954552433/3657830400, 34217723087/696729600, 806539298609929/13168189440000, ...
Cf.
A232193 (numerators of expansion of PolyLog(-1, x)/PolyLog(1, x)),
A232248 (denominators of expansion of PolyLog(-1, x)/PolyLog(1, x)).
-
Table[Denominator[SeriesCoefficient[PolyLog[-2, x]/PolyLog[2, x], {x, 0, n}]], {n, 0, 15}]
Showing 1-3 of 3 results.
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