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A074759 Number of degree-n permutations of order dividing n. Number of solutions to x^n = 1 in S_n. 3
1, 1, 2, 3, 16, 25, 396, 721, 11264, 46089, 602200, 3628801, 133494912, 479001601, 7692266960, 95904273375, 1914926104576, 20922789888001, 628693317946656, 6402373705728001, 182635841123840000, 2496321046987530021, 55826951075231672512, 1124000727777607680001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = n!*coefficient of x^n in expansion of exp(Sum_{k divides n} x^k/k).

MAPLE

A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,

       add(mul(n-i, i=1..j-1)*A(n-j, k), j=numtheory[divisors](k))))

    end:

a:= n-> A(n, n):

seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

MATHEMATICA

Table[a = Sum[x^i/i, {i, Divisors[n]}]; Part[Range[0, 20]! CoefficientList[Series[Exp[a], {x, 0, 20}], x], n + 1], {n, 0, 20}]  (* Geoffrey Critzer, Dec 04 2011 *)

CROSSREFS

Cf. A074351, A261431.

Main diagonal of A008307.

Sequence in context: A092503 A147662 A074182 * A175699 A102882 A085734

Adjacent sequences:  A074756 A074757 A074758 * A074760 A074761 A074762

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 28 2002

STATUS

approved

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Last modified February 25 08:21 EST 2020. Contains 332221 sequences. (Running on oeis4.)