A288312
Number of endofunctions on [2n] such that the image size equals n.
Original entry on oeis.org
1, 2, 84, 10800, 2857680, 1285956000, 880599202560, 853262368358400, 1111400775560275200, 1873276460474747328000, 3967400888465895264384000, 10313998054713896966296473600, 32291970618091110826769565696000, 119851615755915509174015455948800000
Offset: 0
-
b:= proc(n, k) option remember; `if`(k=n, n!,
`if`(k=0, 0, n*(b(n-1, k-1)+b(n-1, k)*k/(n-k))))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..15);
-
Table[StirlingS2[2*n, n]*(2*n)!/n!, {n, 0, 20}] (* Vaclav Kotesovec, Jun 10 2017 *)
-
a(n)=stirling(2*n, n, 2)*n!*binomial(2*n, n); \\ Indranil Ghosh, Jul 04 2017
-
from mpmath import *
mp.dps=100
def a(n): return int(stirling2(2*n, n)*fac(n)*binomial(2*n, n))
print([a(n) for n in range(21)]) # Indranil Ghosh, Jul 04 2017
A209290
Number of elements whose preimage is the empty set summed over all functions f:{1,2,...,n}->{1,2,...,n}.
Original entry on oeis.org
0, 0, 2, 24, 324, 5120, 93750, 1959552, 46118408, 1207959552, 34867844010, 1100000000000, 37661140520652, 1390911669927936, 55123269399790046, 2333521433367183360, 105094533691406250000, 5017514388048998039552, 253135520137219049838162, 13456471561751415850795008
Offset: 0
From _Joerg Arndt_, Jun 10 2013: (Start)
There are a(4-1)=a(3)=24 length-4 words of 3 letters (0,1,2) where adjacent letters are distinct:
01: [ 0 1 0 1 ]
02: [ 0 1 0 2 ]
03: [ 0 1 2 0 ]
04: [ 0 1 2 1 ]
05: [ 0 2 0 1 ]
06: [ 0 2 0 2 ]
07: [ 0 2 1 0 ]
08: [ 0 2 1 2 ]
09: [ 1 0 1 0 ]
10: [ 1 0 1 2 ]
11: [ 1 0 2 0 ]
12: [ 1 0 2 1 ]
13: [ 1 2 0 1 ]
14: [ 1 2 0 2 ]
15: [ 1 2 1 0 ]
16: [ 1 2 1 2 ]
17: [ 2 0 1 0 ]
18: [ 2 0 1 2 ]
19: [ 2 0 2 0 ]
20: [ 2 0 2 1 ]
21: [ 2 1 0 1 ]
22: [ 2 1 0 2 ]
23: [ 2 1 2 0 ]
24: [ 2 1 2 1 ]
(End)
-
Table[n (n-1)^n,{n,0,20}]
-
a(n) = n*(n-1)^n; \\ Michel Marcus, Aug 22 2017
A344053
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k)*k!.
Original entry on oeis.org
1, 1, 0, -9, -40, 125, 3444, 18571, -241872, -5796711, -24387220, 1132278191, 25132445832, 8850583573, -10681029498972, -214099676807085, 1643397436986464, 176719161389104817, 2976468247699317468, -71662294521163070153, -4638920054290748840520, -55645074852328083377619
Offset: 0
-
a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * StirlingS2[n, k] * k!, {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, May 10 2021 *)
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*stirling(n, k, 2)*k!); \\ Michel Marcus, May 10 2021
Showing 1-3 of 3 results.
Comments