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A230345
Number of permutations of [2n+5] in which the longest increasing run has length n+5.
3
1, 12, 181, 3322, 72540, 1845480, 53749920, 1766525760, 64739122560, 2619453513600, 116043825744000, 5588681114016000, 290812286052288000, 16263827918642304000, 973009916329651200000, 62017234027123415040000, 4195886889891954216960000
OFFSET
0,2
COMMENTS
Also the number of ascending runs of length n+5 in the permutations of [2n+5].
LINKS
FORMULA
a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.
a(n) = A008304(2*n+5,n+5) = A122843(2*n+5,n+5).
MAPLE
a:= proc(n) option remember; `if`(n<2, 1+11*n, 2*(2*n+5)*(n+2)*
(n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))
end:
seq(a(n), n=0..25);
CROSSREFS
A diagonal of A008304, A122843.
Sequence in context: A013924 A145560 A332960 * A166773 A202632 A285410
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2013
STATUS
approved