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A194364 The number of n-permutations having precisely two cycles whose lengths are relatively prime. 1
1, 3, 8, 50, 144, 1764, 8448, 89424, 576000, 10628640, 57231360, 1486442880, 11285084160, 196771680000, 2643856588800, 70734282393600, 558255985459200, 22376988058521600, 227061389721600000, 6244741918808064000, 106778305830518784000, 4148476779335454720000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(n) is the coefficient of x^n/n! in the Taylor series expansion of B(A(x)) where A(x)= Sum_{positive integers relatively prime to n}x^n/n and B(x)=x^2/2!.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..200

FORMULA

a(p) = A000254(p-1) for prime p.

MATHEMATICA

f[list_]:=x^First[list]/First[list]+x^Last[list]/Last[list];

Prepend[Table[a=Total[Map[f, Select[IntegerPartitions[n, 2], Apply[GCD, #]==1&]]]; Last[Range[0, n]! CoefficientList[Series[a^2/2!, {x, 0, n}], x]], {n, 3, 30}], 1]

PROG

(PARI) a(n)={sum(k=1, n-1, if(gcd(k, n-k)==1, binomial(n, k)*(k-1)!*(n-k-1)!))/2} \\ Andrew Howroyd, Mar 27 2020

CROSSREFS

Cf. A000254.

Sequence in context: A316797 A000862 A306042 * A338439 A005444 A222684

Adjacent sequences:  A194361 A194362 A194363 * A194365 A194366 A194367

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 12 2011

EXTENSIONS

Terms a(19) and beyond from Andrew Howroyd, Mar 27 2020

STATUS

approved

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Last modified May 12 02:23 EDT 2021. Contains 343808 sequences. (Running on oeis4.)