A246195
Number of endofunctions on [n] where the smallest cycle length equals 8.
Original entry on oeis.org
5040, 362880, 18144000, 804988800, 34488115200, 1482082842240, 65120246231040, 2955402450000000, 139296260790086400, 6837541748945107200, 349978565353512775680, 18685433917574232157440, 1040347501174674201600000, 60368458528123335777196800
Offset: 8
-
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i+1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 8) -A(n, 9):
seq(a(n), n=8..25);
A246196
Number of endofunctions on [n] where the smallest cycle length equals 9.
Original entry on oeis.org
40320, 3628800, 219542400, 11496038400, 570031862400, 27908676956160, 1379187810000000, 69648048665395200, 3619848890071814400, 194427690066299289600, 10817193383227574703360, 624124327363867459584000, 37361601302439627939398400, 2320453709453248711940505600
Offset: 9
-
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i+1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 9) -A(n, 10):
seq(a(n), n=9..25);
A246197
Number of endofunctions on [n] where the smallest cycle length equals 10.
Original entry on oeis.org
362880, 39916800, 2874009600, 175394419200, 9967384627200, 551675124000000, 30471021291110400, 1703458301210265600, 97213825272736972800, 5693251850259515942400, 343266609438110040883200, 21349182724237331665228800, 1371132989012608561874534400
Offset: 10
-
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i+1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 10) -A(n, 11):
seq(a(n), n=10..25);
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