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A230235
Number of permutations of [n] in which the longest increasing run has length 9.
2
1, 18, 287, 4512, 72540, 1209936, 21064680, 383685120, 7315701120, 145957544981, 3044416187213, 66312765615259, 1506481046115907, 35648661471454418, 877558860954150150, 22444760416001869200, 595702609788740888400, 16387438983202886695200
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OFFSET
9,2
LINKS
Alois P. Heinz,
Table of n, a(n) for n = 9..200
FORMULA
E.g.f.: 1/Sum_{n>=0} (10*n+1-x)*x^(10*n)/(10*n+1)! - 1/Sum_{n>=0} (9*n+1-x)*x^(9*n)/(9*n+1)!.
a(n) =
A230232
(n) -
A230231
(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, 9)-b(n, 0, 0, 8):
seq(a(n), n=9..30);
CROSSREFS
Column k=9 of
A008304
.
Sequence in context:
A245924
A368526
A035119
*
A288959
A294327
A286725
Adjacent sequences:
A230232
A230233
A230234
*
A230236
A230237
A230238
KEYWORD
nonn
AUTHOR
Alois P. Heinz
, Oct 12 2013
STATUS
approved
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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)