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A246528 Number of endofunctions on [n] whose cycle lengths are divisors of 8. 2
1, 1, 4, 25, 224, 2601, 37072, 626137, 12232320, 271494865, 6750538496, 185923318329, 5619645500416, 184961854976185, 6585429015521280, 252203521861645561, 10338251689510381568, 451650823526438037153, 20949317446607098716160, 1028215744082428119960025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..350

FORMULA

E.g.f.: exp(Sum_{d|8} (-LambertW(-x))^d/d).

MAPLE

with(numtheory):

egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):

a:= n-> n!*coeff(series(egf(8), x, n+1), x, n):

seq(a(n), n=0..25);

# second Maple program:

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*

      (i-1)!^j, j=0..`if`(irem(8, i)=0, n/i, 0))))

    end:

a:= n-> add(b(j, min(8, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):

seq(a(n), n=0..25);

CROSSREFS

Column k=8 of A246522.

Sequence in context: A268163 A050386 A246524 * A246951 A302587 A302608

Adjacent sequences:  A246525 A246526 A246527 * A246529 A246530 A246531

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 28 2014

STATUS

approved

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Last modified June 13 00:04 EDT 2021. Contains 344980 sequences. (Running on oeis4.)