|
|
A291132
|
|
Number of defective parking functions of length n and defect six.
|
|
2
|
|
|
1, 303, 34660, 2743112, 181875244, 11023248678, 639875755364, 36555471741284, 2090131479753756, 120898503338385149, 7124218746544184628, 429662666436736162636, 26601747798152634836236, 1694092238645618305809580, 111106187207006959809867012
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
7,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (43*exp(1)/720 - 88*exp(2)/15 + 405*exp(3)/8 - 368*exp(4)/3 + 235*exp(5)/2 - 48*exp(6) + 7*exp(7)) * n^(n-1). - Vaclav Kotesovec, Aug 19 2017
|
|
MAPLE
|
S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):
a:= n-> S(n, 6)-S(n, 7):
seq(a(n), n=7..23);
|
|
MATHEMATICA
|
S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];
a[n_] := S[n, 6] - S[n, 7];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|