|
|
A089466
|
|
Inverse hyperbinomial transform of A089467.
|
|
7
|
|
|
1, 1, 3, 18, 163, 1950, 28821, 505876, 10270569, 236644092, 6098971555, 173823708696, 5427760272507, 184267682837992, 6757353631762293, 266191329601854000, 11210291102456374801, 502602430218071545104, 23900770928782913595651, 1201581698963550283673632
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
See A088956 for the definition of the hyperbinomial transform.
a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the functional digraph contains no cycles of length 2. - Geoffrey Critzer, Mar 21 2012
|
|
LINKS
|
|
|
FORMULA
|
A089467(n) = sum(k=0, n, (n-k+1)^(n-k-1)*C(n, k)*a(k)). a(n) = sum(m=0, n, sum(j=0, m, C(m, j)*C(n, n-m-j)*(n-1)^(n-m-j)*(m+j)!/(-2)^j)/m!)).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * n^(n - 2*k) / (k! * (n - 2*k)!). - Daniel Suteu, Jun 19 2018
|
|
MATHEMATICA
|
nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; a=Log[1/(1-t)]; Range[0, nn]! CoefficientList[Series[Exp[a-t^2/2], {x, 0, nn}], x] (* Geoffrey Critzer, Mar 21 2012 *)
|
|
PROG
|
(PARI) a(n)=if(n<0, 0, sum(m=0, n, sum(j=0, m, binomial(m, j)*binomial(n, n-m-j)*(n-1)^(n-m-j)*(m+j)!/(-2)^j)/m!))
(PARI) a(n) = n! * sum(k=0, n\2, (-1/2)^k * n^(n - 2*k) / (k! * (n - 2*k)!)); \\ Daniel Suteu, Jun 19 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|