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A230236
Number of permutations of [n] in which the longest increasing run has length 10.
2
1, 20, 349, 5954, 103194, 1845480, 34288800, 663848640, 13406178240, 282398538240, 6201593613645, 141859542537845, 3376683552323421, 83546513273754977, 2146303277645066980, 57187254952684274700, 1578640101972070456800, 45101111852055549981600
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OFFSET
10,2
LINKS
Alois P. Heinz,
Table of n, a(n) for n = 10..200
FORMULA
E.g.f.: 1/Sum_{n>=0} (11*n+1-x)*x^(11*n)/(11*n+1)! - 1/Sum_{n>=0} (10*n+1-x)*x^(10*n)/(10*n+1)!.
a(n) =
A230233
(n) -
A230232
(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, 10)-b(n, 0, 0, 9):
seq(a(n), n=10..30);
CROSSREFS
Column k=10 of
A008304
.
Sequence in context:
A268787
A272183
A005748
*
A093144
A285393
A156455
Adjacent sequences:
A230233
A230234
A230235
*
A230237
A230238
A230239
KEYWORD
nonn
AUTHOR
Alois P. Heinz
, Oct 12 2013
STATUS
approved
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Last modified April 25 13:26 EDT 2024. Contains 371971 sequences. (Running on oeis4.)