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 A246525 Number of endofunctions on [n] whose cycle lengths are divisors of 5. 2
 1, 1, 3, 16, 125, 1320, 17671, 286336, 5436153, 118144000, 2889312875, 78480441216, 2343333279157, 76274737767424, 2687742759243375, 101931212748928000, 4139544785141163761, 179235455194948829184, 8242391462093927638867, 401202300756829929472000 (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|5} (-LambertW(-x))^d/d). MAPLE with(numtheory): egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))): a:= n-> n!*coeff(series(egf(5), 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(5, i)=0, n/i, 0))))     end: a:= n-> add(b(j, min(5, j))*n^(n-j)*binomial(n-1, j-1), j=0..n): seq(a(n), n=0..25); CROSSREFS Column k=5 of A246522. Sequence in context: A000272 A246527 A159594 * A193242 A247591 A188805 Adjacent sequences:  A246522 A246523 A246524 * A246526 A246527 A246528 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 28 2014 STATUS approved

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Last modified January 20 03:32 EST 2019. Contains 319323 sequences. (Running on oeis4.)