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A335797 a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k!). 2
1, 1, 1, 4, 5, 51, 7, 876, 457, 7678, 5271, 678569, 10705, 27644436, 5060161, 133924576, 197920145, 82864869803, 173283535, 5832742205056, 98269310261, 34660429169122, 25313714237505, 44152005855084345, 13685698802401, 2410161938206898126, 129066382491033573 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of set partitions of [n] into blocks that are relatively prime to n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..576

MAPLE

b:= proc(n, m) option remember; `if`(n=0, 1, add(`if`(

      igcd(j, m)=1, b(n-j, m), 0)*binomial(n-1, j-1), j=1..n))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..27);  # Alois P. Heinz, Oct 12 2020

MATHEMATICA

Table[n! SeriesCoefficient[Exp[Sum[Boole[GCD[n, k] == 1] x^k/k!, {k, 1, n}]], {x, 0, n}], {n, 0, 26}]

CROSSREFS

Cf. A057562, A275429, A335088.

Sequence in context: A042383 A135799 A226648 * A041941 A220534 A341575

Adjacent sequences:  A335794 A335795 A335796 * A335798 A335799 A335800

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 12 2020

STATUS

approved

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Last modified October 18 14:14 EDT 2021. Contains 348068 sequences. (Running on oeis4.)