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A230234
Number of permutations of [n] in which the longest increasing run has length 8.
2
1, 16, 231, 3322, 49236, 761904, 12372360, 211170960, 3788091451, 71356438043, 1409672722481, 29163603260677, 630867328411136, 14247689906846928, 335437110802718232, 8220763598490652440, 209435069840238717949, 5539287889970005834349, 151909981369978722092098
OFFSET
8,2
LINKS
FORMULA
E.g.f.: 1/Sum_{n>=0} (9*n+1-x)*x^(9*n)/(9*n+1)! - 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)!.
a(n) = A230231(n) - A230051(n).
MAPLE
b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
`if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
add(b(u-j, o+j-1, 0, k), j=1..u))
end:
a:= n-> b(n, 0, 0, 8)-b(n, 0, 0, 7):
seq(a(n), n=8..30);
CROSSREFS
Column k=8 of A008304.
Sequence in context: A048445 A028340 A166903 * A274467 A119463 A292341
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 12 2013
STATUS
approved