STATUS
editing
approved
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Revision History for A287899
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Number of permutations of [2n] with exactly n cycles such that the elements of each cycle form an integer interval.
(history; published version)
(history; published version)
MATHEMATICA
Table[SeriesCoefficient[Sum[k!*x^k, {k, 0, n}]^n, {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Aug 10 2019 *)
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
MATHEMATICA
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2]*x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 29 2017 *)
FORMULA
a(n) ~ exp(1) * n * n!. - Vaclav Kotesovec, Sep 29 2017
STATUS
proposed
editing
STATUS
editing
proposed
FORMULA
a(n) = [x^n] (1/(1 - x/(1 - x/(1 - x^2*x/(1 - x^2*x/(1 - x^3*x/(1 - x^3*x/(1 - ...))))))))^n, a continued fraction. - Ilya Gutkovskiy, Sep 29 2017
FORMULA
a(n) = [x^n] (1/(1 - x/(1 - x/(1 - x^2/(1 - x^2/(1 - x^3/(1 - x^3/(1 - ...))))))))^n, a continued fraction. - Ilya Gutkovskiy, Sep 29 2017
STATUS
approved
editing