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A246524 Number of endofunctions on [n] whose cycle lengths are divisors of 4. 2
1, 1, 4, 25, 224, 2601, 37072, 626137, 12227280, 271086625, 6727858496, 184818121929, 5568152828416, 182575550335465, 6473161538599680, 246781048203043561, 10067677495565927168, 437653901985319521153, 20197310874805488471040, 986221173076368356013625 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: exp(Sum_{d|4} (-LambertW(-x))^d/d).
MAPLE
with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(4), 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(4, i)=0, n/i, 0))))
end:
a:= n-> add(b(j, min(4, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);
CROSSREFS
Column k=4 of A246522.
Sequence in context: A246530 A268163 A050386 * A246528 A246951 A302587
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2014
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)