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A230347
Number of permutations of [2n+7] in which the longest increasing run has length n+7.
3
1, 16, 287, 5954, 142590, 3900480, 120466080, 4156079760, 158664456720, 6647965632000, 303540020784000, 15009431909472000, 799414492260384000, 45641465547245568000, 2781538377619921920000, 180263592116387619840000, 12381113998069012804608000
OFFSET
0,2
COMMENTS
Also the number of ascending runs of length n+7 in the permutations of [2n+7].
LINKS
FORMULA
a(n) = (n^3+16*n^2+72*n+71)*(2*n+7)!/(n+9)! for n>0, a(0) = 1.
a(n) = A008304(2*n+7,n+7) = A122843(2*n+7,n+7).
MAPLE
a:= proc(n) option remember; `if`(n<2, 1+15*n, 2*(n+3)*(2*n+7)*
(n^3+16*n^2+72*n+71)*a(n-1)/((n+9)*(n^3+13*n^2+43*n+14)))
end:
seq(a(n), n=0..25);
CROSSREFS
A diagonal of A008304, A122843.
Sequence in context: A299177 A299939 A218517 * A182608 A320763 A225194
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2013
STATUS
approved