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 A246611 Number of endofunctions on [n] whose cycle lengths are multiples of 4. 2
 1, 0, 0, 0, 6, 120, 2160, 41160, 866460, 20294064, 526680000, 15036999120, 468848156040, 15859299473160, 578619457031616, 22654279249875000, 947570269816868880, 42174922731482980320, 1990416896317283627520, 99290011292792071612704, 5220362654145754082460000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 FORMULA E.g.f.: 1/(1-LambertW(-x)^4)^(1/4). - Vaclav Kotesovec, Sep 01 2014 a(n) ~ n^(n-3/8) * sqrt(Pi) / (2^(1/8) * GAMMA(1/8)) * (1 - 11 * sqrt(2/n) * GAMMA(1/8) / (64 * GAMMA(5/8))). - Vaclav Kotesovec, Sep 01 2014 MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1,       `if`(i>n, 0, add(b(n-i*j, i+4)*(i-1)!^j*       multinomial(n, n-i*j, i\$j)/j!, j=0..n/i)))     end: a:= a->add(b(j, 4)*n^(n-j)*binomial(n-1, j-1), j=0..n): seq(a(n), n=0..20); MATHEMATICA CoefficientList[Series[1/(1-LambertW[-x]^4)^(1/4), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *) CROSSREFS Column k=4 of A246609. Sequence in context: A223629 A065888 A246191 * A185757 A075844 A029697 Adjacent sequences:  A246608 A246609 A246610 * A246612 A246613 A246614 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 31 2014 STATUS approved

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Last modified December 5 15:11 EST 2019. Contains 329753 sequences. (Running on oeis4.)